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ESSENTIALS OF PHYSICS 

FOR 

COLLEGE STUDENTS 

A TEXTBOOK FOR UNDERGRADUATES AND A LECTURE COURSE 

AND REFERENCE WORK FOR TEACHERS AND OTHER 

STUDENTS OF PHYSICS 



BY 

DANIEL W. HERING, C.E., Ph.D., LL.D. 

EMERITUS PROFESSOR OF PHYSICS, AND FORMERLY DEAN OF THE FACULTY OP 
THE GRADUATE SCHOOL IN NEW YORK UNIVERSITY 



170 ILLUSTRATIONS 



SECOND EDITION, REVISED AND ENLARGED 



SECOND PRINTING, CORRECTED 



NEW YORK 

D. VAN NOSTRAND COMPANY 

EIGHT WARREN STREET 
1921 



■ 






Copyright, 1918 

BY 

D. VAN NOSTRAND COMPANY 



Copyright, 192 i 

by 

D. VAN NOSTRAND COMPANY 



PRE88 OF 

BRAUNWORTH & CO. 

BOOK MANUFACTURER* 

BROOKLYN. N. V. 



©CU611341 



PREFACE TO SECOND EDITION, 



In this revised edition, the author has corrected typo- 
graphical errors and made changes which no doubt will enhance 
the value of the book. The original purpose has been to present 
the principles of physics in a reasonably complete form, so selected 
as to round out the information of a well-educated man who is 
not aiming to qualify as an engineer or technical expert, but 
who nevertheless desires to be well informed in this branch of 
science. Especially has the author endeavored to make the sub- 
ject of human as well as of technical interest to the student. 
It is hoped that this may help to make the book attractive to 
some who may feel that their knowledge of the subject is be- 
coming impaired, as well as to those who are first acquiring their 
knowledge of it. 

In presenting a subject so broad and so varied as physics, 
no matter what material is selected there will always arise the 
question whether certain things that are omitted would not 
better have been included and others that are included might 
not better have been omitted. No choice can be made that 
will meet with universal approval. Quite as important, it 
seems to the author, is it to present any topic in a way that will 
give the student a proper conception of it and of its relation to 
the rest of the science. 

To accomplish this without a knowledge of higher mathe- 
matics on the part of the reader is a difficult task, and one that 
is definitely limited in its range for want of such knowledge. 
Where the author has felt obliged to stop short of a complete 
exposition, or to omit a rigid demonstration, he has usually 
opened the way for the teacher or student, by reference to more 



IV PREFACE 

extended treatises. These references are of the widest variety, 
from those wholly popular in character to the most narrowly 
technical. However excellent it may be in itself, it is only 
when thus supplemented, at least in some measure, that a gen- 
eral treatise of moderate size can attain its fullest usefulness. 
Instead of giving numerous separate tables of physical data, 
one comprehensive view of physical properties of many com- 
mon substances is appended, in tabular form, and so arranged 
that each column is a table in itself. This will meet, in large 
measure, the occasional desire to refer to such tables, and will 
constitute a valuable addition to the book. The partially 
classified list of books on page x does not include all that are 
referred to in the text, yet this list, even if considerably abridged, 
would provide a student with an admirable library of physics, 
general and special, elementary and advanced. 

D. W. Hering. 

New York University, 
August, 191 7. 



PREFACE TO SECOND EDITION. 

SECOND PRINTING, CORRECTED. 



The exigencies of the great war have forced a development of 
physics along particular lines, notably that of electric signalling. 
The articles treating of this and electric lighting have been re- 
vised, and minor changes have been made, to keep the work in 
accord with the latest practice. 

In revising the Article on wireless telegraphy, the author is 
especially indebted to Dr. Erich Hausmann of the Polytechnic 
Institute, Brooklyn, N. Y., whose suggestions he has been glad 
to follow. D. W. H. 

New York, 
Dec. 15, 1920. 



PREFACE TO FIRST EDITION, 



This work is the outgrowth of a course of lectures which the 
author has delivered for several years past to undergraduate 
students in the University College, in the Collegiate Division, 
and in the Summer School of New York University. 

In the provision that has been made for physics in high 
schools, in universities, and in schools of technology, little regard 
has been had for that considerable class of students preparing 
to fill the position of educated men and women who are not 
specialists in science. 

These should have an opportunity to become acquainted with 
the principles of physics in more than an elementary form, yet 
without the fulness of detail and the more difficult mathematical 
demonstration that would be required by the engineer. 

Although the material in this volume was prepared in the first 
place as a course of lectures, it has been arranged in paragraphs 
and topics to make it suitable also for a textbook of recitations. 

As here given the whole can be included in about sixty lectures 
of fifty minutes each ; but with the text as a basis of recitations, 
the lectures as illustrations, the problems for practice and drill, 
and with occasional tests and a final review, the course may be 
much more extended. On the other hand, it has been found 
flexible enough to make from it a course of half the length by 
judicious selection. 

Sufficient numerical examples are given to illustrate the prin- 
ciples; for more extended problem work, recourse may be had 
to any of the collections of problems published separately. 

No higher mathematics is required than the elements of 
algebra, geometry, and plane trigonometry; and the course may 
be taken with profit by an earnest student who has not studied 



VI PREFACE 

the subject before, but a knowledge of elementary physics would 
be a desirable preparation. In some instances details have been 
purposely omitted, to leave more latitude both to the teacher 
and to the student. 

The experiments suggested for demonstration purposes have 
been placed at the ends of the chapters, so as not to break the 
continuity of the text. 

In most cases experiments of a simple character have been 
chosen, so as to serve the lecturer whose cabinet of apparatus is 
scantily equipped; but any capable teacher will be able to vary 
those here suggested, or increase their number by using others 
more to his liking. Elaborately arranged experiments are 
usually not the kind best suited to the illustration of general 
physics. 

It is hoped that the numerous references throughout the book 
will be of service, especially to teachers. 

The Author tenders his thanks to Dr. Charles Forbes for the 
cut of the Columbia Wave Machine, and to the Scientific 
American, the Weston Electrical Instrument Co., and others 
who have generously contributed material for the illustrations. 

D. W. Hering. 

New York University, 
May, 191 2. 



CONTENTS. 



Preface iii-vi 

Books of Reference . . f x 

CHAPTER I. 

Articles 1-69. 

Properties of Matter; Mechanics 1-84 

Scope and plan of the course; Why study physics? Fundamental con- 
cepts, space, time, matter; Entities of Nature; Significance of dynamics in 
physics; Physics defined; Science and measurement; Units; Physical law; 
Nature and properties of matter; Forms of matter; Stress, force; Laws of 
motion; Inertia; How we know the earth turns round; Measure of force; 
Work, and energy, forms of energy; Central acceleration, centripetal force; 
Simple harmonic motion; Constants of nature; Gravitation, universal law of; 
Why a heavy body falls no faster than a light one; The Cavendish experiment, 
weighing the earth; Center of gravity; Potential energy tends to a minimum; 
Mechanical powers; Moment of a force; Rotation, energy of; Friction; Fluids; 
Liquids, pressure of; Pascal's principle; Center of pressure; Archimedes' 
principle; Buoyancy; Specific gravity, density, methods of determining; 
The celebrated story of "Eureka," the problem of Hiero's crown; Superficial 
energy, surface tension; Pneumatics, expansive tendency of a gas a positive 
force; Atmospheric pressure, barometers; Boyle's law, deviations from; 
Velocity of efflux, aspirating action of flow, Bernoulli's principle; Siphons, 
intermittent springs; Mariotte's flask; Kinetic theory of matter; Mean ve- 
locity of the molecules of a gas; Diffusion; Osmosis and osmotic pressure; 
Brownian movements. Problems. 

Experiments to Illustrate Chapter 1 85-99 

CHAPTER II. 

Articles 70-1 11. 

Heat 100-147 

Temperature; Thermometry; Expansion and contraction; Nature of heat; 
Anomalous behavior of water; Energy in a body in different states; Absolute 
zero; Meaning of heat and temperature by the kinetic theory; Avogadro's 
law; W T ork of expansion of a gas; Combined relation of pressure, temperature, 
and volume, Regnault's (gas) constant; Calorimetry; Specific heat; Freezing, 
a warming process; The two specific heats of a gas; Change of state; Melting 
point, influence of pressure on; Regelation, philosophy of making a snowball, 
movement of glaciers; Latent heat of fusion; Elastic force of vapors; Sat- 



viii CONTENTS 

PAGES 

urated vapor, maximum pressure; Ebullition, boiling point, effect of pressure 
on; Sublimation; Vaporization a cooling process, freezing water by evapora- 
tion; Latent heat of vaporization; Internal work and external work; Crit- 
ical temperature, liquefaction of gases; Spheroidal state; Mean free path 
of molecules; Van der Waal's equation; Hygrometry, dew point, humidity, 
theory of the psychrometer; Atmospheric conditions that make for comfort 
or discomfort; Transference of heat, conduction, convection, radiation; 
Adiabatic curves and ratio of specific heat; Laws of thermodynamics; Dy- 
namical equivalent of heat; Sources of heat; Solar constant. Problems. 
Experiments to Illustrate Chapter II 148-153 

CHAPTER III. 

Articles 11 2-1 20. 

Waves and Wave Motion 154-167 

Generalized sense in which the term wave is used; Waves in liquids, due to 
motion in closed curve; in gases, to longitudinal vibration; in solids, to either 
longitudinal or transverse vibration; Wave front, Huyghens' construction; 
Velocity of propagation, reflection, interference; Stationary waves; Rate 
of travel of (a) gravitational wave, (b) transverse wave in a stretched string, 
(c) wave of condensation and rarefaction in an elastic fluid. Problems. 
Experiments to Illustrate Chapter III , , , 168-169 

CHAPTER IV. 

Articles 1 21-147. 

Sound 170-198 

Sound as a phenomenon and as a sensation; Sound due to longitudinal vibra- 
tion; Velocity in various media; Effect of temperature on velocity of sound; 
Pitch, musical scale, intervals, temperament; Doppler's principle; Intensity, 
quality, fundamental tone, overtones; Kundt's tube determinations; Inter- 
ference of sound, can two sounds produce silence? Beats; Vibrating columns 
of gas; Resonance, wide meaning given to the term; The mouth as a resonance 
cavity; Sympathetic vibration; How we hear; Vibration of air in pipes; 
Vibration of strings; Limits of audition; Musical instruments. Problems. 

Experiments to Illustrate Chapter IV 199-206 

CHAPTER V. 

Articles 148-225. 

Potential; Magnetism and Electricity 207-295 

General principles of potential and fields of force; Their application to 
magnetism and electricity; Physical interpretation of lines of force; Phe- 
nomena of magnets and magnetic substances; Static electrification; Electric 
capacity; Electric induction; Electrophorus; Condensers, energy of charge; 
Lines of force, tubes of force, tubes of induction; Action of a uniformly 
charged sphere externally; Distribution of energy in an electric field; Elec- 
trometers; Current electricity, electric circuit; Potential difference and 



CONTENTS IX 

PAGES 

electromotive force; Sources of electromotive force; Choice of units; Field 
of force about a conductor carrying a current, Oersted's experiment; Gal- 
vanometers; Resistance; ©hm'slaw; Electromagnetic (e.g. s.) units; Practical 
units; Specific resistance; Variation of resistance with change of temperature; 
Divided circuits; How to measure resistance, the Wheats tone bridge; Vari- 
ation of resistance a means of determining temperature; Current sheet; 
Measuring instruments, ammeters, voltmeters, etc.; Heating action of a cur- 
rent, Joule's law, electric determination of the mechanical equivalent of heat; 
Localizing work in a circuit, electric lights and electric lighting; Attraction 
and repulsion of currents; Induced currents, Lenz's law; Magnitude and 
direction of induced electromotive force; Electromagnetic induction, electro- 
magnets; Self induction; The electric dynamo; The electric motor; Induc- 
tion coils, transformers; The telephone and telegraph; Thermoelectricity; 
Chemical effect of a current, electrolysis; Migration of the ions, polarization; 
The voltaic cell; The storage or secondary battery; Displacement currents, 
electric waves; Wireless telegraphy; Discharge of electricity through gases; 
Cathode rays, the electron; Roentgen rays; Radioactivity; Electron theory 
of electricty; Electric actions summarized. Problems. 
Experiments to Illustrate Chapter V 296-305 

CHAPTER VI 

Articles 226-248. 

Light 3 o6- 348 

Nature of light, (a) periodicity, (b) velocity, determined by four methods, 
Roemer's, Bradley's, Fizeau's, Foucault's, (c) character of vibration; Waves 
and rays; Light deviated by reflection, refraction and diffraction; Optics, 
geometrical and physical; Light invisible; The seeing of objects; Images; 
real and virtual; Path of light traced through several media, by waves and 
by rays; Refractive index, critical angle, total reflection; Apparent depth 
of transparent medium; Foci, focal distances of mirrors and lenses; Power 
of lens, images, nearsightedness, farsightedness, selection of lens to correct 
such defect of vision; Photometry; Dispersion, the spectrum, continuous 
and discontinuous; Chromatic aberration; Achromatic lens; Interference of 
light; Color, physical distinction of; Colors of thin plates, Newton's rings, 
Diffraction, measurement of wave length; Polarization; Double refraction; 
Fluorescence; Problems. 

Experiments to Illustrate Chapter VI , ,,,,, ,,.. 349~355 

Table of Physical Data 356-359 

Index 361-367 



BOOKS OF REFERENCE. 

Among the numerous good works on physics in English the following 
would be serviceable for the principles of physics (not laboratory manuals). 
Advanced: 
*Watson's Textbook of Physics. 
*Hastings and Beach, General Physics. 

Daniell's Principles of Physics. 

Barker's Advanced Physics. 

Crew's General Physics. 

Ames' Textbook of General Physics. 

Carhart's University Physics. 
*Ganot's Physics. 
Secondary: 

Mumper's Textbook in Physics. 

Hoadley's Physics (text and laboratory). 
*Millikan and Gale, First Course in Physics (text and laboratory). 
*Carhart and Chute, First Principles of Physics. 
Special: 
*Cajori, History of Physics. 
*Maxwell's Matter and Motion. 

Comstock and Troland, The Nature of Matter and Electricity. 
*Lodge's Elementary Mechanics. 
*Edser's Heat for Advanced Students. 
*Starling's Electricity and Magnetism. 

Wood's Physical Optics. 

Schuster's Theory of Optics. 
*Barton's Textbook of Sound. 

Smithsonian Institution, Physical Tables. 
*Kaye and Laby, Physical and Chemical Constants. 
Questions and Examples: 

Snyder and Palmer, One Thousand Problems in Physics. 
*Shearer, Notes and Questions in Physics. 

Jones' Examples in Physics. 

Miller's Progressive Problems in Physics. 

An excellent treatise, but more advanced than any of the above works 
on general physics, is a Textbook of Physics, in five separate volumes, by 
Poynting and Thomson. 

Hahn's Freihandversuche, I, II, Berlin, is a mine of simple experiments 
illustrating the subject matter of Chapter I, following. 

Of periodicals, apart from the standard journals of physics, both Ameri- 
can and foreign, much valuable information is to be had from School Science 
and Mathematics, Chicago; and Die Zcilschrift fur den physikalischen und 
chemischen Unterricht, Berlin. 

* Those marked with an asterisk would constitute a small but good and com- 
prehensive library of physics. 



ESSENTIALS OF PHYSICS 



CHAPTER I. 
PROPERTIES OF MATTER; MECHANICS. 

i. Physics: Ways of Viewing the Subject. — Physics is likely to be 
viewed in one of three ways: 

(i) By the student who is anxious to master the subject for its own sake, 
it is to be studied in detail, nothing in it being too little to be examined, 
nothing too big to be encountered, no difficulties to be evaded and no simple 
points to be ignored. 

To one who is not thus devoted to the subject this kind of treatment is 
a task not merely unattractive but actually repellent. 

(2) Physics may be studied for the most part as a pure science, but with 
direct and frequent reference to the ways in which it enters into our daily 
experience. For this, the fundamental principles must be learned and 
their relations to one another. The science must be treated systematically, 
but carried only so far as we please; i.e., it must be correct but not neces- 
sarily complete. It is not to be regarded as a mere set of disjointed phe- 
nomena, but all conclusions must rest ultimately upon observed facts. 

(3) Physics may be and sometimes is regarded simply in its applications, 
so called, meaning usually its most obvious applications, such as trolley 
cars, electric lights, an echo, the microscope, etc. This is a superficial and 
inadequate view, because at almost every point in our experience with the 
world around us we come in contact with physics, not always obvious, but 
always there. And, moreover, to attempt to gain a knowledge of physics 
which we can ourselves apply, a more thorough treatment is needed than is 
afforded by a casual study of one or two branches of the subject, because 
in physics, as in any other branch of applied science, it is useless to hope to 
apply what we do not command. One cannot apply mathematics if he has 
no mathematics to apply, nor can he apply physics if he has no physics. 

Therefore, it is the second of these three heads under which we may hope 
to make the study of physics both interesting and profitable. The former 
is comparatively easy to do, and the latter will not be doubtful if questions 
or discussions here given serve to arouse other inquiries or discussions among 
the students. 

1 



2 PROPERTIES OF MATTER; MECHANICS 

2. Why Study Physics? — Partly because it is a subject well worth 
knowing for its own sake, though there are many to whom that idea does 
not appeal. Then, because it affords a kind of training which, it is true, if 
one has only that, will make him as one-sided as any other exclusive line of 
thought, but which is disciplinary in character, and which gives him an 
orderly, logical view of relative values, — a view which rests upon facts 
instead of mere speculation, and the conclusions from which may be verified 
or disproved by facts external to the observer. He can hardly become dog- 
matic. A thing is never so because he says so, but if it is so, no amount of 
disputing on his part can make it otherwise. Thus it is a good corrective 
to arrogance, an incentive to humility, and a support to confidence. 

If this also is an insufficient reason for giving attention to this particular 
branch of science, there is still a third which is more constantly in evidence. 
Physics in some form or other touches human everyday life so continually, 
that one who is ignorant of this subject is in constant danger of blunders 
that make him ridiculous if they do not affect him more seriously. It is 
true that chemistry bears closely upon numerous phases of life and upon 
industrial processes, but chemical actions are molecular in character, and 
not so easy to get at as physical ; biology deals with questions of life itself, 
but these questions are very recondite, and can hardly be approached in- 
telligently without a knowledge of many of the principles of physics. The 
daily experience of everybody is a series of occurrences in physics, and to 
write or to read (especially to write) daily papers intelligently, or to com- 
ment upon the affairs of the day, requires a knowledge of physics. 

It is not pleasant to see an otherwise intelligent person make himself 
ridiculous by ignorance or error in regard to some simple matter of science. 
It is not as if he blundered in a matter of high art, or of deep philosophy, or 
of some special professional ability; for all these are special, and one needs 
not venture into them if he does not choose to do so; but with physics it is 
not so. He cannot get away from that. So long as the atmosphere is for 
us "the breath of life;" so long as the rainbow shall delight the eye, or the 
harmonies of a symphony charm the ear; so long as we shall care to annihil- 
ate time and distance by electric signaling, or avoid weariness by improved 
means of locomotion; so long as civilization shall tend to greater conven- 
ience and comfort of living by applying the forces of nature, — so long shall 
we be under the dominion of physics, and the only alternative by which we can 
escape from it is to revert to barbarism or else to vanish from the earth. 

3. Fundamental Ideas. — Our view of the universe is com- 
prehended in three concepts, viz., space, time,, matter. Each 
has been regarded as a " primary concept," and so not capable 
of definition in more simple terms. 



SPACE — TIME 3 

4. Space. — Space might be regarded as the aggregate of all 
possible answers to the question " Where?" It would thus be 
the sum total of all places or regions, but as these are no sim- 
pler in conception separately than collectively, the idea of space 
is regarded as a primary concept. The concept itself depends 
on our consciousness of exploring, in our own persons, regions 
differently situated relatively to ourselves. " We may add to the 
small region which we can explore by stretching our limbs, the 
more distant regions which we can reach by walking or by being 
carried. To these we may add those of which we learn by the 
reports of others, and those inaccessible regions whose position 
we ascertain only by a process of calculation, till at last we recog- 
nize that every place has a definite position with respect to every 
other place, whether the one place is accessible from the other or 
not " (Maxwell, Matter and Motion, " On the Idea of Space "). 

5. Time. — Like space, time also is treated by the physicist as 
a primary concept, admitting of no definition. As to the idea of 
time, Maxwell suggests that in its most primitive form it is prob- 
ably the recognition of an order of sequence in our states of conscious- 
ness {Matter and Motion). The following, also from the same 
source, is adapted from Newton's Principia, Scholium to Defini- 
tion VIII (q.v.) : " Absolute, true and mathematical time is con- 
ceived by Newton as flowing at a constant rate, unaffected by the 
speed or slowness of the motions of material things. It is also 
called duration. Relative, apparent and common time in duration 
is estimated by the motion of bodies, as by days, months and years." 
And again: " As there is nothing to distinguish one portion of 
time from another except the different events which occur in 
them, so there is nothing to distinguish one part of space from 
another except its relation to the place of material bodies. We 
cannot describe the time of an event except by reference to some 
other event, or the place of a body except by reference to some 
other body. All our knowledge, both of time and place, is essen- 
tially relative." 

Thus we get an idea of intervals of time by associating the 
succession of events with periods of duration. Now if we can 



4 PROPERTIES OF MATTER; MECHANICS 

find that certain kinds of events occur at equal intervals of time, 
we can get a means of measuring time. But we must first have 
a means of deciding the equality of intervals. Experience gives 
us such confidence in Nature's fidelity to herself — in her con- 
stancy — as to lead us to expect that upon the repetition of the 
conditions we shall get like results. 

From the earliest period of history, the succession of day and 
night, and the earth's passage through a cycle of positions rela- 
tively to the sun and stars, have been observed. As the earth 
describes its orbit around the sun, the plane of the meridian 
through any given place on the earth passes through the sun 
three hundred and sixty-five times, before the earth has quite 
reached the position relatively to the sun and stars, from which its 
orbital motion was reckoned. That is, the earth makes 365 + 
rotations relatively to the sun in making one revolution about 
the latter. It makes one more rotation relatively to any of the 
stars, and it makes just as many with reference to one star as to 
another, and between any two instants of observation the same 
portion of a rotation is indicated, no matter to what star it is 
referred. These sidereal rotations are therefore found to be all 
equal in duration. Those with reference to the sun, however, 
are not made in equal periods of time, but the average of all the 
solar periods in one orbital revolution of the earth is called a 
mean solar day, and is taken as a standard for comparing intervals 
of time. 

Suppose a clock to be constructed whose action is not depend- 
ent in any sense upon the position of the earth in its orbit, but 
only upon the earth itself or the materials of which the clock 
is made. Now if the revolution of the earth about the sun is 
repeated in equal periods, and the action of the clock by virtue 
of any qualities of its material is uniform, then the return of the 
earth to any initial position in its orbit will always be correctly 
told by the same number, 365 + days recorded by the clock. 
If the earth's return is irregular and the clock is regular, or vice 
versa, they will in general not agree. If both are irregular, they 
could only agree for all points in the orbit by having their irregu- 



MATTER 5 

larities to vary in precisely the same way, — a state of things 
scarcely conceivable, and the less so when various types of clocks 
are used. In fact they agree very closely, and the agreement 
has been closer as the mechanism of clocks has been improved. 
Their agreement is a strong indication of the constancy in the 
period represented by a day, and in the agencies or in the proper- 
ties of the materials by which the clocks act. It is justly pointed 
out by Maxwell, however {Matter and Motion), that our funda- 
mental conception of time is not based upon the rotation of the 
earth, from the fact that we sometimes ask whether the length 
of the day has changed during the last two or three thousand 
years. (See Garnett's Elementary Dynamics, Chap. I, Arts, i 
and 42.) 

Note. — Astronomers have endeavored to answer the question of invariability 
in the length of a day, with as yet not very accordant results. The conclusion 
reached by the English astronomer, Mr. Adams, and frequently quoted, is that the 
day is growing longer by about 22 seconds in a hundred years. This total gives 
an average of 0.22 second per year for one hundred years, but if the earth's motion 
is undergoing a regular rate of retardation, then in the period of a century the actual 
retardation would change from nothing at the beginning to 0.44 second per year 
at the end, and 0.22 second per year at the middle. Now, as there are 365 \ X 

86,400 seconds in a year, in one second the earth performs — — -r part of 

86,400 X 365 1 

its motion for the year. If it were retarded by one second per year, its rate of rota- 
tion would be diminished by the above fraction of itself, and 0.44 second per year 

would mean a diminution in rate of rotation by of 



100 86,400 X 365 \ 71.7 X io 8 
as compared with its rate one hundred years ago. But a review of Mr. Adams' 
astronomical data by Mr. G. H. Darwin corrects his figures to 23.4 seconds in a 
century, while corresponding data deduced by the late Professor Newcomb give 
as little as 8.3 seconds, or only a little more than one-third as much as Mr. Adams' 
result. The astronomers themselves regard the figures as too uncertain to be 
relied upon with any confidence. (See Thomson and Tait, Natural Philosophy, 
Part II, Art. 830 and Appendix G.) Even taking the largest value given, the rate 
at which the length of the day would seem by that to be increasing is too small to 
be perceived in any ordinary series of observations. 

6. Matter. — We have used the terms " body " and " mat- 
ter " without defining them, but without danger, thus far, of any 
misconstruction. It is sufficient to say of a body that it is " a 
portion of matter which is limited in every direction " (Gar- 
nett, Elementary Dynamics). 



6 PROPERTIES OF MATTER; MECHANICS 

Matter itself is not so easily defined. Attempts to give an 
adequate definition, by metaphysicians as well as by physicists, 
have taken a wide range, from declaring it by the former to be 
not substantial but only ideal, to resting content with the declara- 
tion by the latter that the meaning of matter is a primary con- 
cept, and therefore the term is not capable of definition. With the 
concept once realized as to matter in any form at all, we may and 
must extend our study of matter to all forms of it, whether they 
appeal to any of our six or seven special senses, to all of them, or 
to none. 

Note. — For the propriety of considering a temperature sense apart from the 
sense of touch, see Sir William Thomson's lecture on " The Six Gateways of Knowl- 
edge," Popular Lectures and Addresses, Vol. I. Also, a so-called muscular sense is 
sometimes urged as the means of our becoming cognizant of resistance; but this 
might perhaps be shown to be ultimately the same as the sense of touch, by which 
we become aware of the presence of matter in many of its forms. 

Thus, space involves the idea and determination of the where 
of an event or a thing (and so, of its size) ; time, of the when; and 
matter, of the what and how, and why. 

7. Entities of Nature. — External nature makes us aware of 
only two entities, or things having an objective existence, viz., 
matter and energy; and the latter we are able to recognize only 
in association with the former. We are alike ignorant of the 
ultimate nature of both. Energy may, however, be defined pro- 
visionally as " a capability of matter " in virtue of which any 
definite portion of it may be made to effect changes in other 
definite portions. (See Barker's Advanced Physics, p. 4.) 

8. Significance of Dynamics in Physics. — There is a tendency to rest 
all physical phenomena upon mechanical principles. The late Profes- 
sor Dolbear writes {Matter, Ether, Motion): "As all physical phenomena 
are reducible to the principles of mechanics, atoms and molecules are subject 
to them as much as masses of visible magnitude; and it has become apparent 
that however different one phenomenon is from another, the factors of both 
are the same, . . . matter, ether and motion." It is best, perhaps, not to 
be too sweeping in our generalizations. A later pronouncement upon this 
subject {Elements of Mechanics, Franklin and Macnutt), in a section on 
"The Science of Physics," has this to say: "But what is physics? That 
is the question. One definition at least we must repudiate; it is not 'the 



SIGNIFICANCE OF DYNAMICS IN PHYSICS 7 

science of masses, molecules, and the ether.' Bodies have mass and rail- 
roads have length, and to speak of physics as ' the science of masses ' is as 
silly as to define railroading as the 'practice of lengths,' and nothing as rea- 
sonable as this can be said in favor of the conception of physics as the science 
of molecules and the ether; it is the sickliest possible notion of physics even 
if a student really gets it, whereas the healthiest notion, even if a student 
does not wholly grasp it, is that physics is the science of the ways of taking 
hold of things and pushing them! " But if this is a fact, we must not forget 
that the mere statement of a truth about anything is not the same as giving 
a definition of it. 

In the first chapter of the excellent manual, Glazebrook and 
Shaw's Practical Physics, the authors say: " We cannot then do 
better than urge those who intend making physical experiments 
to begin by obtaining a sound knowledge of those principles of 
dynamics which are included in an elementary account of the 
science of matter and motion. For us it will be sufficient to refer 
to Maxwell's work on Matter and Motion as the model of what 
an introduction to the study of physics should be." 

So fully is all this now recognized as to make it the basis of 
the distinction between physics and chemistry, so far as a dis- 
tinction is required. Without making such a distinction we 
have Maxwell's statement {Matter and Motion, Chap. VI) : "The 
discussion of the various forms of energy, — gravitational, electro- 
magnetic, molecular, thermal, etc., — with the conditions of trans- 
ference of energy from one form to another, and the constant 
dissipation of the energy available for producing work, consti- 
tutes the whole of physical science in so far as it has been de- 
veloped in the dynamical form, under the various designations 
of Astronomy, Electricity, Magnetism, Optics, Theory of the 
Physical States of Bodies, Thermodynamics and Chemistry." 
Darnell's Physics opens with the statement, " Natural philosophy, 
or physics, may be briefly defined as the science of matter and 
energy." The author, however, recognizing that this necessarily 
includes chemistry and biology, proceeds to the closer definition 
of physics as " the systematic exposition of the phenomena and 
properties of matter and energy in so far as these phenomena can 
be stated in terms of definite measurement and explained by 



8 

reference to mechanical principles or laws" thus placing physics 
more upon the basis of mechanics. 

The distinction between physics and chemistry is further elabo- 
rated by both Professor Daniell and Professor Barker through a 
further extension of this idea. That is, chemistry is regarded 
as the science of matter as to its forms and transformations, 
while physics is the science of energy as to its forms and trans- 
formations. The former has for its fundamental principle the 
conservation of matter, the latter the conservation of energy. 
The two overlap in this wise : // changes in matter are studied with 
especial reference to the phenomena of energy involved, it is 
chemistry, but it is specified as physical chemistry; if changes of 
energy are studied with especial reference to the kinds of matter 
concerned, it is physics, but is specified as chemical physics. 

The intimate association of matter and energy is further seen 
in the fact that no change in matter can be effected without a 
simultaneous energy-change of some form, so that every chemical 
change necessarily involves physical changes ; but the converse 
of this is not true. 

9. Definition of Pliysics. — Evidently, therefore, physics re- 
gards matter solely as the vehicle of energy. And hence, from 
this point of view, physics may be defined as that department of 
science whose province it is to investigate all those phenomena 
of nature which depend either upon the transference of energy 
from one portion of matter to another, or upon its transformation 
into any of the forms which it is capable of assuming. In a word, 
physics may be regarded as the science of energy, precisely as 
chemistry may be regarded as the science of matter. (Barker, 
pp. 5 and 6.) Physics is not, however, to be regarded as simply 
a number of detached phenomena. 

10. Science and Measurement. — It has been aptly said 
that " science is measurement," for although intelligent ideas as 
to the kinds of relations subsisting between supposed causes and 
effects are often important and sometimes necessary to further 
investigation, in advance of the exact statement of natural 
laws, yet knowledge cannot be called truly scientific until those 



UNITS — PHYSICAL LAW 9 

relations can be expressed in numbers. To this end it is neces- 
sary to be able to measure each thing, whether cause or effect, 
so as to compare the measurements. Measurement always 
involves the idea of difference; either a difference between two 
things, or between two states of the same thing. Physics as 
an exact experimental science depends upon the detection and 
measurement of change, either as to the amount of change or 
rate of change. 

"When you can measure what you are speaking about and express it in numbers, 
you know something about it; but when you cannot measure it, when you cannot 
express it in numbers, your knowledge is of a meager and unsatisfactory kind; it 
may be the beginning of knowledge, but you have scarcely, in your thoughts, ad- 
vanced to the stage of science, whatever the matter may be " (Sir William Thomson, 
Popular Lectures and Addresses, Vol. I, p. 80). 

1 1 . Units. — For measurement are required units, since a 
unit is that physical magnitude that is applied to another magni- 
tude of the same sort to determine its size. All the interactions 
that occur between bodies can be ultimately expressed in terms 
of three fundamental magnitudes as factors, involved to various 
degrees. When measurements are expressed in such terms they 
are called absolute measurements, and a system of units of vari- 
ous kinds, each of which is defined in terms of the three funda- 
mental quantities, is called an absolute system of units. The 
absolute system in common use in science is known as the centi- 
meter-gram-second (c.g.s.) system, and is based upon the centi- 
meter as the unit of length, the gram as the unit of mass, and 
the second as the unit of time. (See Glazebrook and Shaw, 
Practical Physics, pp. 17 to 24.) 

12. Physical Law. — Our confidence in the constancy of 
Nature, which constancy is the basis of the laws of Nature, is 
sometimes expressed by the statement that " the same causes 
will always produce the same effects." This expresses a physical 
impossibility, since no event ever occurs more than once, and 
Maxwell explains the meaning of the statement to be that " if 
the causes differ only as regards absolute time or the absolute 
place at which the event occurs, so likewise will the effects," and 
submits the following as a more explicit statement of the prin- 



IO PROPERTIES OF MATTER; MECHANICS 

ciple: " The difference between one event and another does not 
depend on the mere difference of the time or the places at which 
they occur, but only on differences of the nature, configuration, 
or motion of the bodies concerned " (Matter and Motion, p. 31). 
The relation which any event bears to the " nature, configura- 
tion, or motion of the bodies concerned," or the relation between 
the above-named " differences," is what is meant by a physical 
law. 

13. Nature and Properties of Matter. — A definition which 
should embody a statement of the essential character of matter 
has often been attempted by metaphysicians as well as by physi- 
cists. Tait, Properties of Matter, pp. 12 and 13, and Appendix I, 
gives numerous such definitions and hypotheses (q.v.), but says 
for himself that " an exact or adequate conception of matter 
itself, could we obtain it, would almost certainly be something 
extremely unlike any conception of it which our senses and our 
reason will ever enable us to form." 

It is probable that there are some, and possible that there are 
many, forms of matter of which we are not cognizant because we 
have no especial sense organ to appreciate them, or have not yet 
recognized the conditions favorable to making them appreciable 
by the organs which we have. 

It is not, however, always necessary to have a special sense 
organ to perceive a special form of matter. We may be assured 
of the existence of the matter, by knowing that it performs func- 
tions which are exclusively those of matter, and we may learn 
something of its attributes by the manner in which it performs 
those functions. (See Maxwell, Matter and Motion, " Test of 
a Material Substance," pp. 165, 166.) Vortex motion in a hy- 
pothetical perfect fluid gives to the portions in motion distinct 
properties which may serve so to distinguish these portions from 
other portions not in such motion as to constitute what we call 
matter, that is, to make a distinction between a material sub- 
stance and a nonmaterial substance. (See Holman's Matter, 
Energy, Force and Work, Chap. IV. Read from Watson's Phys- 
ics, last half of Art. 124, "The Constitution of Matter.") 



FORMS OF MATTER II 

Experiment No. r, p. 85. — Vortex Rings. To form the rings, place 
side by side in the box a vessel containing a little hydrochloric acid, pref- 
erably warmed (or else a little common salt on which is poured sulphuric 
acid), and one containing strong ammonia. Remember that the ammonium 
salt thus formed has nothing to do with the rings except to make them visible. 

14. Forms of Matter. — Although the ultimate nature of 
matter is unknown, its structure and the forms under which we 
encounter it are to a considerable extent familiar. Possibly 
there is but one primitive and primary form, of which all others 
are modifications; but matter as we know it presents itself under 
five so-called forms or states (sometimes called states of aggrega- 
tion), viz., solid, liquid, gaseous, ultragaseous, and ethereal, and 
in each, except perhaps the last, there are various kinds of matter 
differing in certain distinctive characteristics or " properties." 
But each kind of matter is continuous at least throughout the 
range of the first-named four states of aggregation. 

Paying no heed for the present to any question of molecules 
and their relative motions, or freedom to move, we may recog- 
nize purely physical distinction of solids, liquids and gases. 

The first division of matter as to form is into solid and fluid; 
the latter, again, into liquid and gaseous forms. " A body that 
will sustain a longitudinal pressure, no matter how slight, with- 
out lateral support, is a solid; one that will not thus sustain 
pressure is a fluid." Also, " A liquid is a fluid with which a vessel 
may be partly filled; a gas will wholly fill a vessel though but 
a small quantity be introduced " (Maxwell). These conceptions 
are sufficient for all dynamical considerations of matter. Under 
them fluids may be harder than solids. 

Illustrations. — A rod of tallow will sustain a small longitudinal pressure 
without giving way or needing lateral support. It is thus a soft solid. 
Pitch, though hard, will yield under the slightest pressure, in time, unless 
supported laterally. It is a hard fluid. Its mobility is increased (or vis- 
cosity diminished) by addition of turpentine. 

Most gases are invisible, but are usually perceptible by the 
sense of smell. They can contain and transmit energy, as shown 
by steam or air under pressure. 



12 PROPERTIES OF MATTER; MECHANICS 

Ultragaseous matter is shown by Crookes' tubes. A compari- 
son of the electric discharge through Crookes' tubes and Geissler's 
tubes shows difference not in the matter itself but in the states 
of aggregation. The same is shown by the long Crookes' tube 
containing caustic potash. This when warmed reduces the vac- 
uum and the matter changes from ultragaseous to gaseous. But 
ultragaseous form is vehicle of energy, as shown by radiometer, 
mill-wheel tube, etc. (Lecturer exhibit.) 

Ether is not perceptible to the senses, but is a vehicle for the 
transmission of energy, especially heat and light, or radiation. 
Radiant energy would pass across a space that is a vacuum, or 
that contains quiet material like air or water at rest, or that has 
matter like air or water sweeping through it in either direction; 
so that ether is the vehicle of energy apart from the other matter 
traversed. If that matter obstructs or checks the radiation, then 
it acquires the energy of which the ether separately was possessed. 
Example : The sun's energy radiated to the earth. 

15. Stress. — Actions between different portions of matter, 
so far as we know, always produce motion or a change of motion 
in bodies as a whole, though the body be but a molecule or an 
atom; or else they produce distortion, which is a movement of 
some parts of a body relatively to the other parts. In the case 
of molecular motions, they may be interpreted to our conscious- 
ness as sound, heat, light, or other physical phenomena; but 
motion or deformation of extended bodies we appreciate physio- 
logically in the first instance by a sense of pulling or pushing, — a 
sense of exertion sometimes called our muscular sense. No body 
has ever been known to move itself or change its motion in any 
way, but only to undergo such effect when under the influence of 
some other portion of matter and in turn exerting a corresponding 
influence upon it. And, further, no body has ever been known 
to fail in moving under the influence of any portion of matter if 
free from all other external influences of a restraining nature. 

The mutual action between two portions of. matter is called 
stress, and may exist between different bodies or between differ- 
ent portions of the same body. 



FORCE 13 

Tlie tendency of a body to fall to the earth, or of the earth to 
fall to the sun, is ascribed to an action of the earth and the body, 
or of the sun and the earth, upon each other called the attrac- 
tion of gravitation; and although the nature of this action 
is not understood, it is believed to take place between them 
in some way by stress through the medium of the universal 
ether. 

The stress subsisting between the molecules of any given sub- 
stance is called an attraction of cohesion, which may possibly be 
of the same nature as gravitation. (See Thomson's Popular Lec- 
tures and Addresses, Vol. I, lecture on " Capillary Attraction," 
Appendix B.) 

The mutual actions of magnetized bodies or of electrified 
bodies upon one another are called attractions or repulsions as 
the bodies are influenced to approach or to separate from one 
another, and are also supposed to indicate a stress in the ether 
as the medium connecting the bodies. 




Fig. 1. Stress in Coiled Spring. 

16. Force. — Stress viewed as affecting one of the bodies or 
one of the parts between which the stress exists is force. In 
Fig. 1, A and B are bodies between which is the spring I in a 
state of tension or compression. A and B may be the hands of 
the experimenter. They are each subjected to a force as well as 
L. The force on A or that on B is one aspect of the stress 
existing in the spring connecting the two bodies. It must be 
remembered that a stress of any kind is always dual in character. 
Two bodies or two parts of one body are always concerned in it, 
and if one pushes or pulls upon the other, so the other pushes or 
pulls equally upon the one. The stress, viewed in its relation 
to one body, is frequently called the action upon that body, while 
the reciprocal relation is called the reaction by the same body or 



14 PROPERTIES OF MATTER; MECHANICS 

upon the other body. Action and reaction always exist together, 
being two aspects of one and the same stress, and are evidently 
equal. Action and reaction occur between bodies. 

Instances are abundant and varied. A book supported on 
the hand exerts pressure, but the hand reacts upon the book to 
hold it up, or if it is descending, to hold it by just so much as its 
slow fall is attended by pressure on the hand. One cannot push 
open a door without pushing back upon the floor; he cannot 
press in the piston of an air chamber without a corresponding 
pressure from the piston upon the hand. The recoil of a gun 
when discharged is due to the reaction corresponding to the 
action of the powder on the bullet. In the case of bodies not 
contiguous, as magnets or electrified bodies which exert attrac- 
tion or repulsion, the action is mutual; and so with astronomical 
bodies. If the earth attracts an apple, equally the apple attracts 
the earth. (Perhaps neither " attracts," but whatever the action 
between them, it is considered as mutual.) In all cases the ac- 
tion and reaction between the bodies are equal and opposite; 
no matter what the nature of the bodies acting upon one an- 
other, or what the medium connecting them and through which 
the action is transmitted, the stress acting upon either body 
is force, and so far as we can tell is of only one sort: we do not 
know of different kinds of force. 

Stresses themselves, and therefore force as one aspect of a 
stress, are consequences rather than causes; but as the effect upon 
either body concerned, so far as regards motion or distortion, is 
always commensurate with the stress that is developed, instead 
of saying that the action of other bodies upon the one under 
consideration has caused the ensuing motion or distortion, it is 
customary to say the motion or distortion is in obedience to the 
force or is caused by it. In this way the force is regarded as the 
agent and its magnitude is determined by the effect upon the 
body. Forces are then said to act upon bodies with various 
intensities, at different points and in any direction; and thus 
conventionally all phenomena of mechanics have been referred 
to the fictitious agency of forces. 



FIRST LAW OF MOTION 15 

The convention is convenient enough to justify its retention, even when 
we recognize its fictitious character; so the misuse of terms serves to avoid 
tiresome circumlocution, and is general, but only excusable on the ground 
of convenience. (See further on this subject, W. K. Clifford in Nature for 
June 10, 1880; also Soddy, Matter and Energy, pp. 105-108.) 

Where it is practicable we shall generally prefer to regard 
forces as exerted upon or applied to bodies instead of acting 
upon them. 

Since the only consequence of the application of force is a 
change in a body with respect to its motion if it is free to move, 
or with respect to its size or shape or both if it is not free, the 
change of the body in either of these respects might be made a 
means of comparing or measuring forces. We should reach the 
same value for the same force by whatever method we employ 
to measure it, and therefore either of these two will answer, 
provided they always agree with each other. Generally the one 
depending upon the motion of bodies is preferred. We need 
only in the outset so far assume the permanence of the properties 
of matter as to treat equal moderate distortions of a spring as 
equal manifestations of force; also to assume that, other condi- 
tions being the same, the mass of different portions of homo- 
geneous material is proportional to their volume. 

17. First Law of Motion. — Every body continues in its state 
of rest or of uniform motion in a straight line, unless it is compelled 
by impressed force to change that state. 

This law is also known as the law of inertia, since it states that 
no body alters its state of rest or motion without the interven- 
tion of some outside influence ; and this fact we express in scien- 
tific language by saying tersely that " matter has inertia." 

Inertia, then, is a general property of matter with the excep- 
tion, possibly, of ether, which is itself a limiting form of matter. 
Inertia is implied in the first law of motion. As we shall see, its 
character is that of a time function of matter rather than a quan- 
titative property of matter. But because some bodies require a 
greater force than others to bring them to a given motion very 
quickly, they are said to possess greater (or more) inertia, and 



1 6 PROPERTIES OF MATTER; MECHANICS 

some writers (as Thomson and Tait, construing Newton) go to 
the length of saying that " matter possesses an inherent power 
of resisting " the agent that is brought to act upon it. 

Note. — This is much like the so-called electrical resistance which a substance is 
supposed to possess because it does not perfectly conduct; and matter, in like 
manner, can be said to resist motion only because it does not facilitate it. 

In this view inertia is sometimes treated quantitatively, and 
masses are compared by their inertias, the inertia itself being 
determined by the force necessary to overcome it in any stated 
measure. But the only measure possible is the velocity ac- 
quired, and this in its turn is dependent upon the length of time 
during which the body is acted upon. With all this understood, 
it is possible to build up a consistent system of masses, forces, 
and motions on inertia as a basis; but where mass is of chief 
consequence in ultimate results, it is also possible and more 
convenient to regard inertia simply as a fact concerning matter 
rather than as a measurable property of matter, and then meas- 
ure masses by a direct comparison as to forces and resulting 
accelerations. 

This seems the more reasonable because matter does not resist, 
it yields. It is not as if a body refused absolutely to yield or to 
move until the force applied to it reached a certain magnitude, 
and then it suddenly started off at a definite speed. The slightest 
force is able to move (overcome the inertia of) the greatest mass, 
and we prefer to say, then, that the rate at which the motion is 
changed is dependent not upon the inertia but upon the quantity 
of matter. In our view masses are the things considered, masses 
having already been defined, and may be measured without 
regarding inertia quantitatively if the latter is only viewed as a 
fact common alike to all matter. 

To say that a large amount of matter has more inertia than a small 
amount is like saying that in a silent house a large room has more silence 
than a small one, or that in a dark hall one portion has more darkness than 
another portion, or that a dead elephant has more death than a dead mouse. 
Even if it does require more light to illuminate a large room than a small one 
to the same degree, when the least amount of light is admitted into the 



HOW WE KNOW THE EARTH TURNS ROUND 17 

largest of rooms some illumination is effected and it is no longer dark; and 
so, too, when the slightest force is applied to the greatest mass it moves it. 
The decisive point, and that which brings both modes of treatment to the 
same result, is that a definite length of time is necessary to bring about a 
definite change of motion. The body which in one statement has the 
slightest finite amount of inertia, or in the other the least finite mass, would 
require an infinite force to give it a finite velocity instantaneously. This 
gradual bringing up of a body to a given speed is expressed by Professor 
Lodge as "reluctance of matter to change its state," but this is to intimate 
that matter will not rather than cannot so change. Perhaps the former is 
true; the latter is in accord with ordinary views. The fact is simply that 
matter does not change its state of itself. 

The fact of inertia, then, is expressed in the statement that a 
finite force gives to a finite mass a finite velocity only in a finite 
time; if time is infinitesimal, mass must be infinitesimal or force 
must be infinite. If time is infinite, mass may be infinite or 
force infinitesimal. 

Examples of inertia : Pulverizing small masses by sharp blows 
in mid-air, destruction from collision unless buffers, air cushions 
or springs are interposed, etc. 

Experiment No. 2, p. 85. — The breaking of a cord above or below a 
weight suspended from it, to show, first, the fact of inertia, and next, the 
part time plays in it. 

Experiment No. j, p. 86. — Ball or coin on a card. When card is slowly 
moved it carries the object along; suddenly flipped, it leaves the object un- 
disturbed. 

Experiment No. 4, p. 86. — Rigidity of chain on pulley to show both 
inertia and the fact that motion confers upon the chain properties it did not 
possess when at rest. 

18. How We Know the Earth Turns Round. — Inertia has 
been employed to demonstrate the rotation of the earth upon 
its axis. If the earth rotates, the top of a tower or mast moves 
faster than the bottom. The dome of the Pantheon in Paris is 
272 feet above the floor; the latitude is 48° + , and for the earth to 
rotate in 24 hours the top T, Fig. 2, moves to the east faster than 
the bottom P moves, 0.18" per second. A body requires 4.1 
seconds to fall from the top of the dome to the floor. Theoreti- 



i8 



PROPERTIES OF MATTER; MECHANICS 




Fig. 



2. Proof of the Earth's 
Rotation. 



cally it should strike 0.75" to east of point under plummet. By 
repeated experiments a ball thus dropped always fell to the east 

from J" to 1". 

This experiment may be inter- 
preted either way, for if we regard 
the rotation of the earth sufficiently 
well proved, we may regard this as 
confirming the principle of inertia. 
(For fuller statements on this par- 
ticular subject see Hall in Physical 
Review for September, 1903; and 
also Cajori, History of Physics) 

FoucauWs Pendulum Experiment. 
— The most celebrated demon- 
stration of the rotation of the earth is by a method devised 
by Leon Foucault. A pendulum set oscillating in a given plane 
will, owing to the principle of inertia, continue to oscillate in the 
same plane no matter how its 
point of suspension may be 
turned. 

Let A and B (Fig. 3) be two 
positions of a dial fixed in a 
horizontal plane, i.e., tangent 
to a meridian. Suppose a pen- 
dulum to be set oscillating in 
the meridian plane AP and to 
trace a mark across the dial 
beneath it. As the absolute 
direction of oscillation will not 
be altered, when the dial moves 
to B the trace first made will 
now be in the line BP, but if 
the pendulum now makes a 
trace it will be in the line BS, 
parallel to its original direction of swinging in space, or at an 
angle with the trace BP equal to the angle APB or a. 



w 



M/ 




rr 

/ / / 
i\i 


1 
1 
1 

l 

1 


/ jjsB^ 










JB 


C \ 











Fig. 3. Demonstration of the Principle 
of Foucault's Pendulum. 



FORCE OF INERTIA — SECOND LAW OF MOTION 19 

Draw AR and BR in the plane perpendicular to the axis CP\ 

call AR = BR = r; and AP = BP = p;. angle ARB = 0. a = 

arc AB . arc ,4£ ,. .,. « r . , DDD , . , 

; )3 = ; dividing, - = - . Angle 5Pi? = latitude, 

p r (3 p 

X, and- = sin X; therefore, a = sin X. For one hour of rota- 

tion |S should equal 15 ; therefore, the hourly rotation of the dial, 
or the angle a, should equal 15 X sin X. Results of carefully 
conducted experiments agree closely with this. At New York, 
latitude 40 50', the hourly angle should be 9 48'. 

Experiment No. 5, p. 86. Foucault's Experiment. 
Examples. — 

1. At New York University, latitude 40 52', the angle described by a 
Foucault pendulum in fifty minutes was 8° 20' ; what does this give as the 
period of the earth's rotation? Ans. 23 hrs. 33 min. 

2. If the earth rotates in 24 hours, what is the hourly angle described by 
the pendulum at the poles? What at the equator? 

19. Is There Such a Thing as "Force of Inertia?" — No, 

if we mean a definite force appertaining to a definite body, a 
resistance which must be overcome before the body's state of 
motion can be altered ; for any force will change the motion (over- 
come the resistance) of any body, and, on the other hand, we 
know of no instance in which a body's motion was changed by 
its inertia. The force employed in overcoming the inertia of a 
given body depends upon the time allowed for producing a defi- 
nite change in the rate of motion. If inertia were a resistance, 
then with a given inertia no change of motion would occur until 
the applied force reached a definite amount, as in the case of 
friction, where the force of friction increases with the increase 
in the applied force until the latter is sufficient to overcome the 
maximum value of the former. 

20. Second Law of Motion. — While the first law cites inertia 
in a negative manner, the second law presents the other side 
and shows the responsiveness of matter to the application of 
force. It says: 

Change of motion is proportional to the impressed force, and takes 
place in the direction in which the force acts. 



20 PROPERTIES OF MATTER; MECHANICS 

This law also is an expression of the behavior of bodies due to 
inertia, but the quantitative relation of force and motion is 
determined by the quantity of matter in the body and the time 
rate of change in its motion. Observe, however, that this law 
declares not a reluctance but a willingness of matter to yield to 
the application of force; not a refusal but a compliance; not an 
opposition but an obedience. No instance is known of the 
refusal of a free body to obey the application of a force in chang- 
ing its state of rest or motion. 

This law gives us to understand that if several forces are applied 
to a body simultaneously the body follows the law with regard 
to each force, finally reaching a place or a condition to which it 
might have been brought by one single force. Such single force 
is called the resultant of the given forces. The forces may be 
represented by vectors, and the resultant obtained by vectorial 
addition, or by geometrical construction thus: 

Let two forces, applied at a point, be represented in mag- 
nitude and direction by two straight lines drawn to scale; 
their resultant, i.e., a single force that would accomplish just 
what these two do, would be represented by the diagonal of 
the parallelogram of which the lines representing the given 
forces are adjacent sides. This process of uniting two forces 
into one is called the composition of forces, and is not restricted 
to two, but may be extended to any number of forces. A body 
to which such forces are applied will be held in equilibrium 
by a single force that is applied at the same point, and which 
is equal to their resultant in magnitude and opposite to it 
in direction. 

From this it is easy to see that any force may be replaced 
by two others that are applied at the same point as the given 
force, and are represented by two sides of a parallelogram if 
the given force is represented by the diagonal. This process 
of separating one force into two others, styled components, is 
called the resolution of forces, and may be extended until the 
given force has been resolved into any number of components. 
The commonest method is to resolve the force into two compo- 



SECOND LAW OF MOTION 21 

nents at right angles to each other. These are rectangular com- 
ponents, and the parallelogram then becomes a rectangle. 

By velocity is meant the rate at which space is traversed; and 
the average velocity v is the ratio of the distance s to the time t 

occupied in traversing the distance; or, v = ~, The velocity of 

a moving particle at any instant is measured by the distance that 
would be traversed by the particle in a unit of time (say one 
second), if the particle moved on for the one second without 
going faster or slower. 

An exact idea of velocity includes direction of motion as well as dis- 
tance and time, the term "speed" being used for the rate of travel when 
direction is disregarded; but the distinction is not adhered to rigidly. A 
body may move at a given rate or with a given speed, but the phrase "rate 
of speed" is meaningless and should be avoided. 

If the velocity of a moving body is changed its motion is said 
to be accelerated, and the measure of the acceleration is the rate 
at which the velocity is altered. If the increase or decrease of 

v 
velocity in the time / is v, the acceleration is -. In general, since 

acceleration is the velocity gained or lost per second, if a body 
starts from rest the velocity at the end of one second will equal 
the acceleration, at the end of two seconds twice the accelera- 
tion, and after / sees. / times the acceleration; i.e., if accelera- 
tion is/ and velocity acquired is v, then v = ft. If the velocity 
acquired in t sees, from nothing amounts to v, then the average 

v 
velocity for these t sees, is — , and the distance traveled is the 

2 

average velocity X time, or, under uniform acceleration, dis- 
tance s = \jt X t = \fi 2 . If the acceleration is that of gravity 
g, and space is height h, h = \gt 2 . 

Examples. — 

i. An aeronaut flies from Paris to Rheims, a distance of 160 km., in 2§ 
hours. What is his average speed? Ans. 60 km. per hr. 

2. A body travels 900 meters in 1^ hours. Show that its average velocity 
is 20 cm. per second. 



22 PROPERTIES OF MATTER; MECHANICS 

3. A body has a velocity of 50 cm. per second; 6 seconds later its veloc- 
ity is 290 cm. per second. By how much was the velocity changed? 

Ans. 240 cm. per second. 

4. Using the term " acceleration " to indicate the rate at which velocity 
is changed, what was the acceleration in Ex. 3? 

Ans. 40 cm. per sec. per second. 

5. A body has a velocity of 50 cm. per second forward; 8 seconds later 
it has a backward velocity of 190 cm. per second. What is its acceleration? 

Ans. —30 cm. /sec. 2 . 

Motion as mentioned in the second law is to be understood as 
Newton explained it, viz., the combined measure of mass and 
velocity, i.e., their product, which we call momentum; and it is 
the change of this in a given time that is proportional to the 
force that is acting during that time; or, the force itself is pro- 
portional to the rate of change in momentum. 

Momentum is the effect on the body, due to the force; the action 
of .the latter is measured by the force taken in conjunction with 
the time it is in effect; i.e., by their product, which is called the 
impulse. 

Impulse expresses the action that produces the effect. The 

second law of motion declares the equality of impulse and the 

momentum it produces. If velocity is changed from v to V\ and 

the mass is M, momentum is changed by M (vi — v ) , and if this 

was effected by a force F in the time t, we have the equation 

Ft = M(vi — Vq). If the body starts from rest and is brought to 

the velocity v, or starts with the velocity v and is brought to rest, 

the change of momentum is Mv; and 

Ft = Mv. 

, change of momentum ,.>. 

Hence force = — -; (A) 

time 

= time rate of change of momentum. 
Again, the equation might be written, 

but - is rate of change in velocity and is called acceleration, hence 
1 

force = mass X acceleration. (B) 



MEASURE OF FORCE 23 

21. Measure of Force. — (A) and (B), Art. 20, show at once 
how to measure force and what is a unit force. From (A), force 
may be determined at any instant by the rate at which momen- 
tum is then being altered; or if the change of momentum, either 
gaining or losing, is going on uniformly for a length of time, the 
average force is equal to the entire change of momentum divided 
by the time during which the change is effected. (B) gives the 
same result by multiplying the mass by the rate at which velocity 
is being altered; or in prolonged uniform change of velocity, by 
dividing the entire change of velocity by the entire time, and 
multiplying this quotient by the mass moved. The result thus 
determined will be the number of units of force only under the 
definition of unit force as the force which will give to unit mass 
unit velocity in unit time. It presupposes the definition of unit 
mass, unit distance, and unit time. In common usage there is 
but one unit time, — the second ; there are two standard units of 
mass in use, — the English, called the pound, and the French, the 
gram; and there are two units of length, — the English foot and 
the French centimeter. In the English units, unit force is such 
force as will give one pound a velocity of one foot per second in 
one second; it is called a poundal. In the French units, unit 
force is such a force as will give to one gram of matter a velocity 
of one centimeter per second in one second; it is called a dyne. 
These are so-called " absolute units " of mass, length, time, 
velocity and force. Another set, known as gravitation units, is 
presented in a table on p. 32, Art. 24. Here we may simply say 
that the weight of a pound is about 32.2 poundals, and the weight 
of a gram about 980 dynes. 

Note. — If a moving body is stopped by impact with another body, the question 
what is the force of the blow delivered is too indefinite to admit of an answer. It 
depends upon the time required to stop the body, i.e., to change its momentum 
from something to nothing; or else upon the distance passed over in bringing the 
body to rest. 

Some interesting examples may be drawn from common 
experience. 

(a) What additional pressure is exerted upon the surface of 
the earth (or a roof), by falling rain? 



24 PROPERTIES OF MATTER; MECHANICS 

On the afternoon of July 5, 1901, New York was visited by 
a phenomenal downpour of rain. During the storm there was 
one period of five minutes in which the rainfall amounted to 
0.38 inch. To compute the effect on one square foot of surface, 
this depth of 0.38 inch would have a mass of 2 pounds, or 
m = 2. If we assume that the average velocity with which the 
drops strike the earth is 100 feet per second, or v = 100, the 
momentum mv, destroyed in five minutes (or 300 seconds) by 
one square foot of surface, is 2 X 100 = 200 units. The average 

force, then, F = ■ — = 0.67 poundal per square foot. On a 

building 50 feet by 100 feet this would make 3350 poundals, 
or a weight of a little over 100 pounds. On an acre the force 
would be 29,040 poundals, or 902 pounds — nearly half a ton 
in weight. 

When we come to consider the pressure of a gas according to 
the Kinetic Theory, we shall have recourse to precisely the same 
form of computation. 

(b) The principle that force equals the rate of change of 
momentum serves to show that the force with which the wind 
presses against a surface varies as the square of the velocity of 
the wind; for doubling the velocity doubles the mass of air that 
impinges in a unit of time, and as the mass has double velocity 
the momentum destroyed per unit of time is 2^X211 = 4 mv, 
or four times the original momentum. Similarly, if velocity 
is trebled, momentum equals 9 mv; quadrupled, 16 mv; and 
so on. 

(c) If a car have a given velocity and at the beginning of each 
of 60 successive seconds a man weighing 150 pounds steps aboard, 
how much greater force must the motor supply that the speed 
may not be diminished by this steadily increasing load? 

If v = velocity (say 10 ft. per sec), and m = 150, the momen- 
tum to be added each second is mv = 1500; and since Ft = mv, 
F X 1 = 1500, whence F = 1500 poundals, or 50 pounds, nearly. 
This does not mean that the additional force is to be applied 
every time a person gets on, but that if such force were added 



COMPARISON OF FORCES AND OF MASSES 25 

without the accession of passengers there would be an increase 
of speed; and against this the calculated rate of increase in 
momentum would just equalize the increased force and keep the 
speed constant. 

(d) From Watson's Physics, p. 881 : " A small sphere of mass 
one milligram travels backwards and forwards between two paral- 
lel planes with a constant speed of 1000 cm. /sec. If the distance 
between the planes is 5 cm., find the force which must be applied 
to the planes to keep them from moving under the influence of 
the impacts. Obtain this force (1) supposing the diameter of 
the sphere to be negligible, and (2) when the diameter of the 
sphere is 2 mm." 

m = 0.001 gram; distance traveled from one impact to the 
next against the same plane = 10 cm. ; time to go this distance = 

= 0.01 sec; change of velocity on impact = 2000 cm./sec; 

1000 

change of momentum = mv = 0.001 X 2000 = 2 units; as this 

2 



occurs in 0.01 sec. the change of momentum per second is 

0.01 

200; this is the measure of the force against the plane, which is 

therefore 200 dynes. 

If the diameter of the sphere is 0.2 cm., the distance traveled 

between impacts is 2 X 4.8, or 9.6 cm.; the time for this is 

-^— , or 0.0096 sec. ; the change of mv per second is , or 

1000 0.0096 

208.3, an d the force is 208.3 dynes. 

22. Comparison of Forces and of Masses. — From the second 
law we see that if a force be applied to various bodies, by a 
fixed distortion of a given spring, their masses will be propor- 
tional to the accelerations they receive, and equal masses will be 
those which receive equal acceleration under the same or equal 
forces. If two masses whose equality has thus been established 
be subjected to various forces, these forces will be proportional 
to the accelerations they produce ; and equal forces will be those 
which give to the same mass or to equal masses equal accelera- 
tions. 



26 PROPERTIES OF MATTER; MECHANICS 

23. Third Law of Motion. — To every action there is always 
an equal and contrary reaction; or the mutual actions of any two 
bodies are always equal and oppositely directed. 

This has already been considered in the treatment of stress, 
and might as well have been stated first as third. 

Note. — In the fuller consideration of what Newton meant by the terms "action " 
and "reaction," it appears that he included much of what is now treated under the 
equivalence of work and energy. 

For illustration of second and third laws of motion, etc.: 

Experiment No. 6, p. 88, shows that a body obeys each force im- 
pressed upon it as if others were not also impressed on it, by the fact that 
two balls dropped from a given point reach the floor at the same time, 
though one has a horizontal impulse and the other has not. 

Experiment No. 7, p. 2>^, using spring balance for forces, shows result- 
ant of two forces, or three forces in equilibrium. 

Examples. — (For Examples 1 to 7 refer to Arts. 20 and 21.) 

1. A force of 980 dynes acts upon a mass of one gram for one second. 
What velocity does it generate? Ans. 980 cm. per sec. 

2. A force of 1,000,000 dynes acts upon a body for 20 seconds and gives 
it a velocity of a meter per second. What is the mass of the body? 

Ans. 200,000 grams. 

3. How long must a constant force of 150 dynes act upon a kilogram to 
generate in it a velocity of 30 cm. per second? Ans. 3 min. 20 sec. 

4. What force acting upon a mass of 120 grams for one minute will 
produce a velocity of 35 cm. per second? Ans. 70 dynes. 

5. A jet of water impinges perpendicularly against a wall with a velocity 
of 20 meters per second. If 50 kg. of water strike the wall each second, 
what pressure will be exerted against the wall (a) if the water does not 
rebound; (b) if it rebounds with a velocity of 5 meters per second? 

Ans. (a) io 8 dynes; (b) 1.25 X io 8 . 

6. A mass of 50 grams is moving with a velocity of 90 cm. per second. 
After a certain force has acted upon it for 5 seconds, its velocity is 250 cm. 
per second. How great is the force? Ans. 1600 dynes. 

7. A mass of 49 grams moving at the rate of 20 meters per second is 
opposed by a force of 980 dynes. In what length of time will this force 
bring the body to rest? Ans. 1 min. 40 sec. 

8. A ball weighing 500 grams falls upon a steel slab with a velocity of 
500 cm. per second and rebounds with a velocity of 400 cm. per second. 
What is the average force between the ball and the slab if the impact 
occupies Tffo sec? Ans. 45 million dynes. 



WORK AND ENERGY 27 

9. A spring stretched to a certain elongation pulls upon a mass of 1000 
grams, free to move, and in 2 seconds gives it a velocity of 50 cm. per second; 
the same force gives to another body in 5 seconds a velocity of 200 cm. per 
second. What is the mass of the second body? (Art. 22.) 

Ans. 625 grams. 

10. Two forces Fi and F 2 , of 3000 dynes and 4000 dynes respectively, at 
right angles, both in the plane of the paper, are applied to a particle. Con- 
struct a diagram to scale, and determine from the diagram, and also by cal- 
culation, the magnitude and direction of a third force that will hold the 
particle in equilibrium.. (Experiment No. 7.) 

Ans. 5000 dynes, making an angle with Fi of 126 52 V 

11. In Fig. 33b, what is the pull on the horizontal chain, and the thrust 
on the oblique strut, to support a suspended weight of 800 grams, if the 
horizontal chain (and balance) is half as long as the oblique strut? Solve 
by drawing and numerically. 

Ans. Horizontal, 462 grams; oblique, 924 grams. 

24. Work and Energy. — (For this entire subject refer to 
Barker's Physics, Chap. Ill; or to Maxwell, Matter and Motion, 
Chap. V, pp. 101-106, middle paragraph of p. 107, and on to 
p. no, then pp. 133 and 134; but for this course give simply the 
following.) 

" Work is the act of producing a change of configuration in a 
system (or body), in opposition to a force which resists that 
change" (or when force is required to produce such change). 
Something, therefore, is moved when work is done. The work 
is measured by the product of the force by the distance through 
which it moves the body on which work is done. 

" Energy is the capacity for doing work." 

A material system is a conservative system; i.e., when work is 
expended on the system to change its configuration, it possesses 
then additional energy by which it is capable of doing an exactly 
equal amount of work, in regaining its former condition. Poten- 
tial energy is its energy due to any advantage of position it may 
have as a whole or in the distribution of its parts (configuration) . 
Kinetic energy is energy due to motion, and energy in either of 
these divisions may belong to a body en masse, or to its molecules 
individually. 



28 PROPERTIES OF MATTER; MECHANICS 

" All kinds of energy are so related to one another that energy 
of any kind can be changed into energy of any other kind." 
This is the correlation of energy. 

" When one form of energy disappears, an exact equivalent, 
of other form or forms, always takes its place, so that the sum 
total of energy is unchanged." This is the conservation of energy. 
As thus stated, the changes of energy must not be confounded 
with the effect produced if the system of bodies under considera- 
tion be affected by extraneous forces as additional. The total 
amount of energy in any body or given system of bodies is 
constant, unless the system is acted upon by forces from without. 
In such case the change of energy is at the expense of some other 
system (producing the change) by an exactly equal amount, and 
so it results in saying that the total energy in the universe is 
an unchanging and unchangeable quantity. The form of energy 
and the way in which it is manifested may alter, but not the 
grand total, stated by Maxwell thus: "The total energy of 
any material system is a quantity which can neither be increased 
nor diminished by any action between the parts of the system, 
though it may be transformed into any of the forms of which 
energy is susceptible." Now, considered as deduced from obser- 
vation and experiment, that, of course, only asserts that no sys- 
tem has yet been discovered in which the principle is not true, 
but "asa science-producing doctrine it is always acquiring ad- 
ditional credibility from the constantly increasing number of 
deductions which have been drawn from it, and which are found 
in all cases to be verified by experiment. If, by the action 
of some agent external to the system, the configuration of the 
system is changed, while the forces of the system resist this 
change of configuration, the external agent is said to do work on 
the system. In this case the energy of the system is increased 
by the amount of work done on it by the external agent. If, on 
the contrary, the forces of the system produce a change of con- 
figuration which is resisted by the external agent, the system is 
said to do work on the external agent, and the energy of the 
system is diminished by the amount of work which it does. 



CORRELATION AND CONSERVATION OF ENERGY 20. 

" Work, then, is a transference of energy from one system to an- 
other; the system which gives out energy is said to do work on the 
system which receives it, and the amount of energy given out by 
the first system is always exactly equal to that received by the 
second. If, therefore, we include, both systems in one larger 
system, the energy of the total system is neither increased nor 
diminished by the action of one partial system on the other." 
The doctrine of the conservation of energy has been declared 
" the one generalized statement which is found to be consistent 
with fact, not in one physical science, but in all. 

" When once apprehended, it furnishes to the physical inquirer 
a principle on which he may hang every known law relating to 
physical actions, and by which he may be put in the way to dis- 
cover the relations of such actions in new branches of science " 
(Maxwell, Matter and Motion) . 

The facts that any form of energy may have an exact equiva- 
lent in any other form, and that there is no absolute destruction 
of energy, would lead us to suppose that perpetual motion, for 
instance, would be not only possible but inevitable; and it would 
be possible if we could always control the exact character of 
energy that would result in the case of any transformation, but 
that we cannot do. The different modes in which energy is 
manifested, as muscular effort, chemical action, heat, etc., form, 
as it were, a succession of steps by which energy descends from 
a higher to a lower plane. Such descent is called degradation. 
Energy can be fully changed from a higher to a lower form, but 
in attempting to restore it we succeed in restoring only a part, 
the remainder reappearing in a still lower form, and thus not 
available for the accomplishment of work requiring the higher 
form of energy. It follows, therefore, that a degradation of energy 
is thus continually going on, and we are obliged to confront the 
startling prospect that eventually energy, on the earth, will exist 
only in one form. That form in which it is continually reappear- 
ing as a residuum is heat. 

To illustrate external and internal work, as also conservation 



3Q 



PROPERTIES OF MATTER: MECHANICS 



I 

o 
o 
o 
o 
o 
o 
o 
o 



ffi 



0^ 



of energy: If the system, Fig. 4, is in equilibrium, S is under 
stress and has potential energy of strain. If W 2 is drawn down 
while Wi is held, energy is increased 
in S. The work thus done may be 
seen by releasing W\ while W 2 is kept 
in its lowered position; Wi rises a 
measurable height h corresponding to 
work WJi and increasing the energy 
of Wi relatively to the earth by that 
amount. The total energy of the 
system, including the earth, is now 
the same as originally, since the en- 
ergy of position of W 2 is less than at 
first by just so much as that of Wi is 
greater; and the energy of S is the 
same as at the beginning, the whole 
system being again in equilibrium. 
There is no change in the energy of a 
system by action between the parts themselves. 

A change in the potential energy of a system is the equivalent 
of the work done in changing the configuration of the system. 

A change in kinetic energy is the equivalent of the work done 
in changing velocity. 

If a force F is steadily applied to a body of mass m, the latter, 

starting from rest, acquires in the time / a velocity v, and passes 

over a distance s equal to that which it would have traversed in 

v 
the same time with the average velocity - ; i.e., 



■JK. 



Fig. 4. 



Transference of 
Energy. 



= -*, 

2 



and since F = m - (Art. 20), multiplying these two equations 
t 

member by member, 



Fs 



J mv 2 . 



Fs is the measure of the work done by the force F, and | mv 2 is the 
measure of the kinetic energy lost or gained by the body upon 



CORRELATION AND CONSERVATION OF ENERGY 3 1 

which the work is done. Therefore, F = , or — ^ . Hence, 

5 s 

force may be regarded as the space rate of doing work or of trans- 
ferring energy. 

The various forms in which energy is manifested may be ar- 
ranged in two groups as follows: 

"I. Potential Energy : 

1 . Strain, whether extension, compression or distortion. 

2. Gravitative separation. 

3. Chemical separation. 

4. Electrical separation. 

5. Magnetic separation. 

II. Kinetic Energy: 

1. Translatory or rotatory motion. 

2. Vibration, including sound. 

3. Radiation, including light, etc. 

4. Heat, both latent and sensible. 

5. Electricity in the form of current." — Barker. 

Energy of strain is shown in a bent or wound-up spring. The 
energy is displayed as the spring is relaxed, doing work, and 
" strain " disappears. Energy of gravitative separation is in a 
raised weight or a waterfall; the energy is displayed when the 
body descends and there is no longer " separation." Energy of 
chemical separation is in carbon and oxygen when apart. The 
energy is evidenced when they combine, burning, and the " sepa- 
ration " gives place to combination. There is energy of electrical 
separation when the earth and a cloud are oppositely charged, 
and the electricities are separate. The work of effecting this 
separation was gradual and quiet but cumulative; energy is dis- 
played when the lightning stroke occurs, and " separation " gives 
place to combination. Energy of magnetic separation is the 
equivalent of the work required to separate two magnetic poles, 
and then they can do work by reason of being separate. 

Similarly, illustrations may be given of energy due to motion. 
These latter forms are all evidenced in the work or physical 



32 



PROPERTIES OF MATTER; MECHANICS 



change they are able to effect; e.g., i,.in the work required to 
deprive a body of its motion, or the resistance the body can over- 
come in moving through a distance; 2, the internal or molecular 
work by which vibrations are steadily damped, or the production 
of sound; 3, heat produced by the interception of radiation; 4, 
mechanical work accomplished by heating a gas; 5, magnetic 
and heating effects of a current. 

Under I, Nos. 1, 2, 4 and 5 are distinctly mechanical; and like- 
wise under II, Nos. 1 and 2 are reducible to the mechanical form 
in most cases, and always expressible as the product of two 
factors. (See Lodge's Elementary Mechanics, Art. 93, p. 118; 
also article on " Energetics " in New International Encyclopedia.) 

Note. — Mechanics we may understand to be that portion of physical science 
which deals with the action of matter upon matter, so far as such action affects the 
motion, size or shape of bodies, no matter how large or how small they may be. 

Mechanical actions are such actions as affect the motion, size or shape of bodies, 
no matter how large or how small they may be. 

We are now prepared for a systematic .view of the three princi- 
pal dynamic units. 

Scheme of Units. (Discuss.) 



Absolute. 


Gravitation. (See Art. 21.) 




Metric 
c.g.s. 


British f.p.s. 


Metric c.g.s. 


British f.p.s. 


Mass 

Force 

Work 


Gram. 
Dyne. 
Erg. 


Pound. 

Poundal. 

Foot-poundal. 


980. 2 grams. 
Gram weight. 
Gram-centimeter. 


32. 2 pounds. . 
Pound weight. 
Foot-pound. 



A force of 980.2 dynes equals the weight of one gram at New 
York. 

Note. — It must be remembered that force and mass cannot both be expressed 

as pounds in the same problem. If mass is pounds, then force is poundals, and 

32.2 poundals equals the weight of one pound. On the other hand, if it is desired 

... . . ... . . lbs. weight 

to express the force in pounds, the mass will be the . 

32.2 

In like manner, in c.g.s. units, if mass is grams, force is dynes, and 980.2 dynes 

equals the weight of one gram, but if it is desired to express force in grams, then 

gms. weight 



the mass will be 



980.2 



CORRELATION AND CONSERVATION OF ENERGY 



33 



Energy of position is often converted into that of motion, as 
in a descending pendulum, or the weights of a clock; in water fall- 
ing to drive machinery; also strain is so converted when springs 
impel a mechanism. 

Energy of motion is converted into energy of position in ascend- 
ing pendulum or other body, and owing to inertia it may be seen 
in mobile substances as liquids; e.g., when water is taken into the 
tank of a locomotive by the motion of the latter (Fig. 5). The 











mm, 



Fig. 5. Tender of Locomotive taking Water while in Motion. 

energy of motion of the train is expended to increase the energy 
of position of water, relatively to the earth, by lifting it from the 
track to the tank of the engine, if the speed is sufficient for the 
height. To lift any mass m requires a force nig; to raise it a 
height h, work equal to mgh must be done. Enough energy must 
be supplied by the velocity v that \ mv 2 = mgh; i.e., if the train 
stood still and the water flowed into the feed pipe, it would 
require a speed v, giving it energy \ mv 2 equal to mgh; v repre- 
sents the relative speed of train and water. If the latter is sta- 
tionary, then v is speed required by the train. The equation gives 
v = V2 gh, and taking g to be 32 ft. /sec. 2 , if h is, say, 8 ft., then 
v = 22.5 ft. per second, or 15.3 miles per hour, making no allow- 
ance for friction of the water in the pipe. 

(Example from College Entrance Examinations. — A weight w descending 
a height h drives a pile into soil a distance d. Find the average resistance 
of the pile. 

If the weight w is the force, say pounds, and h the height, say feet, w 
expends energy equal to wh foot-pounds. If d is the distance, also in feet, 



34 PROPERTIES OF MATTER; MECHANICS 

which the pilejs driven while offering a resistance of r pounds, the work is 

rd foot-pounds. Since wh = rd, r = — -.) 

d 

Examples. — 

i. A bag containing 50 kg. of sand lies on a scaffold 25 meters above the 
ground, (a) What is its potential energy relatively to the ground? (b) It 
falls; what is its kinetic energy when it strikes the earth? (c) What is its 
velocity? (d) What is its momentum? 

Ans. (a) 1225 X io 8 ergs. 

(b) The same. 

(c) 2213.6 cm. /sec. 

(d) 11,068 X io 4 gm.-cm./sec. 

2. A bullet of mass 120 grams is discharged with a velocity of 400 meters 
per second from a rifle, the barrel of which is one meter in length. What is 
the energy of the bullet when it leaves the muzzle, and the average pressure 
exerted upon it within the barrel by the exploding powder? 

Ans. Energy, 9.6 X io 10 ergs. Force, 9.6 X io 8 dynes. 

3. How much work must be done on a mass of one ton to give it a ve- 
locity of 20 feet per second? (g = 32.) Ans. 12,500 foot-pounds. 

4. What is the energy of a train of 40 tons, moving at the rate of 30 miles 
an hour? What force will bring it to a stop in a distance of 500 feet? 

Ans. 2,420,000 foot-pounds; 4840 pounds. 
Two equal masses are at the top of two inclined planes of the same 
height but unequal lengths. Which mass has the greater potential energy, 
relative to the base of the plane? If both slide down without friction, which 
will have the greater velocity on reaching the base? 

6. A baseball whose mass is 150 grams and velocity is 2000 cm. /sec. is 
stopped by the hand of the catcher in mov- A E 

ing back 30 cm. after impact. What is the ^^" 

average pressure of the hand against the / 

ball? (Suggestion, Fs = \ mv 2 .) / 

Ans. 10,000,000 dynes. / 

25. Central Acceleration; Centrip- 1 
etal Force. — A body moving uni- \ 
formly in a circular path of radius \ 
r with speed v has a central accelera- \^^^ 

v 2 F 

tion - as shown thus: Fig . 6 . Central Acceleration. 

In Fig. 6, AB = small arc described in time /; then AB = vt. 
In time of going from A to B the body has descended towards 



SIMPLE HARMONIC MOTION 35 

center the distance AD; this is the extent of departure from 
the direction of the original motion while describing the actual 
path AB. If velocity in circumference is uniform, so also is this 
change in direction toward center, or central acceleration. Call 
this acceleration /. Then in time /, AD = \jt 2 (see p. 21); 
and AF = 2 r. If AB represent a very short distance, it is virtu- 
ally equal to the chord. Also in triangle ABF, AB 2 =ADxAF; 
or, substituting values, 

1 v^ 
v 2p. _ 2 r x -ft. 2 , whence, / = — 

2 r 

By the first law of motion, the body would only be deflected 

from the tangential path by the application of some force, the 

effective component of which is at right angles to the tangent or 

towards the center of the circle. The measure of this force is the 

ffiv 2 
product of the mass by the acceleration, or ; and the reaction 

which the body exerts against such force is known as centrifugal 
force. It is necessarily equal and opposite to the centripetal 
force. 

Experiment No. 8, page 89. Centrifugal Force. 
Examples. — 

1. A mass of 200 grams is whirled round in a circle at the end of a string 
120 cm. long, fastened at the center of the circle, at a rate of 2 revolutions 
per second. What is the pull upon the string? 

Ans. 379 X io 4 dynes, or 3866 grams. 

2. A car of 20 tons is moving round a circular curve of 1000 feet radius 
at a speed of 40 miles per hour. What is its outward pressure against the 
track? Ans. 137,671 poundals, or 4275 pounds. 

26. Simple Harmonic Motion. — This may be defined pro- 
visionally as the projection of uniform circular motion upon a 
diameter. A body moving with S.H.M. has an acceleration that 
is proportional to its displacement. 

Let P, Fig. 7, be a point moving with uniform velocity v in 
circle of radius r. A point as M, traversing the diameter AB, 
exactly keeping pace with P, will describe S.H.M. through the 
center 0. The distance of M from is called the displacement. 




36 PROPERTIES OF MATTER; MECHANICS 

If co is the angular velocity of P, v = no. For any position of P 
call the angle POA = 6. If T is the period of one complete 
revolution of P or of one complete l 

2 IT 

to-and-fro movement of M, T = 

CO 

The acceleration of M along AO 

is equal to the parallel component 

of the acceleration of P along PO. B 

The acceleration along PO, by pre- 

. v 2 
ceding article, is — , which equals 
r 

— or rco 2 . This, multiplied by the Fig . 7 . Simple Harmonic Motion. 

cosine of POA, gives the acceleration of M along AO. 

„~ . OM displacement 

cos POA = — - = — • 

OP r 

.*. Acceleration along AO = co 2 X displacement. 

Q.E.D., since co is constant; and this law of acceleration may be 
used to define Simple Harmonic Motion. 

Now the period of the S.H.M. is T = — ; 

CO 

. rr, 4 /displacement 

whence 1 = 2tt\ — —, ; 

T acceleration 

Since a body moving with S.H.M. has acceleration proportional 
to displacement, it is always under a force which varies as the 
displacement (for force varies as acceleration) . Under dynamics 
the converse of this is shown to be true, viz., a body subject to a 
force varying as its displacement has S.H.M. 

But this law of variation of force is a law of elasticity (as deter- 
mined by experiment), therefore elastic bodies or bodies whose 
movement is controlled by an elastic medium- describe S.H.M., 
or have vibratory motion. The actual motions of vibrating elas- 
tic bodies or parts of bodies, then, are periodic and consist of 



SIMPLE HARMONIC MOTION 



37 



one or a combination of more than one S.H.M. The diagram of 
S.H.M. is the sinusoid. 




Wave Form representing Simple Harmonic Motion. 



In Fig. 8, if abscissae (or horizontal distances from OY) repre- 
sent time, and ordinates (or vertical distances from OX) displace- 
ments, then for a particle moving in DC with S.H.M. beginning 
at O, the curve representing one complete vibration has the wave 
form OEF. The motion of A to which the S.H.M. along DC 

corresponds may be circular, or 
elliptical, with longest axis verti- 
cal, reaching the path CD as its 
limit, in which case the vibration 
is said to be transverse (i.e., to 
the direction OF in which waves 
due to the motion of O proceed) ; 
or the longest axis may be hori- 
zontal, reaching the path AB as its 
limit 7 in which case the vibration 
is longitudinal. 

The pendulum is an approxi- 
mate example of S.H.M. If the 
bob is at A, Fig. 9, with mass m, 
the force is mg acting vertically. The component of g acting in 
the path AO is g sin 0. For small values of d, sin oc 0. The 
displacement is AC X = Id = OA. 
The period of complete swing is 




Fig. 9. The Simple Pendulum. 



2 Try 



Id 
gsin 



in which 



sin0 



38 PROPERTIES OF MATTER; MECHANICS 

approaches unity as its limit as 6 decreases, so that for an in- 
finitesimal arc / = 2 7r y -. Thus t is dependent only on / and g. 

s 
In strict S.H.M., where the ratio of displacement -f- acceleration 
is constant, T is the same for any amplitude, or vibrations large 
or small are isochronous. 

Examples. — 

i. At New York the length of a simple pendulum beating seconds is 
99.3 cm. If it is shortened one millimeter, how much will it gain in one 
day? Ans. 43.2 seconds. 

2. How many swings per minute will be made by a simple pendulum 
20 feet long? (Take g = 32 ft. /sec. 2 .) 

3. Assuming the length of the seconds pendulum to be 98 cm., find the 
length of a pendulum in the same locality that will oscillate 120 times in 
30 seconds. Ans. One-sixteenth of the length of the seconds pendulum. 

4. By how much must a pendulum be shortened to make it oscillate 
twice as rapidly? 

27. Constants of Nature. — We often speak of the con- 
stancy of nature, and we sometimes speak of the necessity of 
stating natural processes in some definite measure, some exact 
quantitative terms whereby we distinguish physics as an exact 
science. The possibility of doing this leads us to the knowledge 
and use of so-called " constants of nature." It must be under- 
stood, however, that the constancy of these " constants " re- 
quires that well-defined conditions shall be met. Examples are 
the freezing or the boiling point of a liquid; the coefficient of 
expansion of a substance, or its elasticity, or its density; the 
dielectric constant of a medium, or its refractive or dispersive 
power, etc. Volumes of these constants have been compiled for 
reference. 

One of the most important of these quantities is the accelera- 
tion due to gravity; meaning here by " gravity" the attraction of 
the earth. This is usually symbolized by g. It means the rate 
at which the velocity of a freely falling body increases. It is 
not a force, therefore, but it is numerically equal to the number 
of units of force which gravity exerts upon a unit mass. 



CONSTANTS OF NATURE 



39 




Fig. 10. Determination of g by 
Helical Spring. 



A helical spring, Fig. 10, if ex- 
tended, will develop a force that 
is proportional to the extension. 
If a weight whose mass is m be 
suspended from such a spring, it 
will produce a definite elongation, 
say e, coming to rest at 0. With 
this elongation, the force pulling 
on the weight by the spring is 
just equal to the weight, or 
mg. If the weight be drawn fur- 
ther, as to D, and then released, 
it will oscillate through the mid- 
position O under a force that 
varies as its distance from 0; 
i.e., it will have S.H.M. If 



A , having mass m, were describing the circle of reference A CBD 



2-KY 



in the period of oscillation T, its velocity would be — - , and, as 



its acceleration towards the center is 



, this becomes ^— , and 
i 2 



the force directing it towards the center is m times this, or 



4 T z mr 

2^2 



or 



force 



4 w z m 



, r being the extreme distance from the mid- 



r T 2 

position in the S.H.M. of M. But in S.H.M. for any displace- 
ment x, of the oscillating body, the ratio of the force F to the 
-p 

displacement x, or — = const., sometimes called the " spring 
x 

constant." Thus in this oscillating weight, when the displace- 
ment is e the force is mg, and 



mg 
e 



4 7T Z 



whence g 



4 7r 2 e 



j>2 > ° y 1 

Experiment No. g, page 90. — By measuring the elongation produced in 
such a spring by any weight, and timing the oscillations of that weight, the 
above equation determines g. 



40 PROPERTIES OF MATTER; MECHANICS 

It must be remembered, however, that in the above discussion 
the effect of the mass of the spring itself upon the period of oscil- 
lation is ignored, so that a determination of this kind is only 
approximate, and not very close unless the period of the spring 
itself is negligible. 

28. Gravitation; Why a Heavy Body Falls No Faster than 
a Light One. — The falling of a body to the earth is attrib- 
uted to the earth's attraction for it, and the weight of the body 
is a force that is the measure of that attraction. 

It is observed that in a vacuum all bodies fall at the same rate, 
i.e., with equal accelerations. (This is not saying they are all 
equally attracted by the earth.) They are all subjected to the 
attraction of the same body, the earth, and at the same distance 
from it (i.e., from its center). We have seen that in accordance 
with the second law of motion the acceleration of a body is 
proportional to the force and inversely proportional to the mass, 

F 

or a = k — . Now with various masses M, the acceleration, a, 

M 

could not be the same unless the force F varied in just the same 

F 

proportion that M varied, that is, unless — is constant; so that 

if the accelerations are alike, as shown by experiment, then the 
ratio of F to M for each and all is the same, and hence the at- 
traction of the earth for bodies, i.e., their weight, is proportional 
to the quantity of matter in them, i.e., their mass. This force, 
therefore, or the weight, is a proper basis for the comparison of 
masses. 

Newton established the fact that the earth attracts bodies 
with a force that is proportional to their mass, by suspending 
hollow spheres of the same size from strings of equal length, 
filling them with various substances, and observing that they all 
swung in the same period, i.e., with equal accelerations under the 
earth's attraction (Principia, Bk. Ill, Prop. VI, Theorem VI). 
Such an experiment helps to confirm the second law of motion; 
but if we consider the law as sufficiently well established and also 
that the attraction of the earth for any body at a given place is 



UNIVERSAL LAW OF GRAVITATION 4 1 

proportional to the mass of the body, then these principles would 
demonstrate that necessarily a heavy body and a light one would 
fall at the same rate. For by heavy (gravis) we mean having 
gravitation force, and so the force F due to gravity varies just as 
the mass M of the body; or for all bodies the ratio of the force of 

p 

gravity to the mass, or — , is constant. But this ratio, by the 

second law, is the acceleration due to gravity. 

Experiment No. 10, page 90, with water hammer, shows that the liquid 
falls in bulk as a solid, or when it breaks into drops at the throat the drops 
fall with a click, like a metal. Also bodies falling in a vacuum tube. 

29. Universal Law of Gravitation. — Newton's experiments 
with the pendulum showed that the attraction of the constant 
body, the earth, at a constant distance from another body 
varied as the mass of the other body, but this was only a 
partial expression of the general law of gravitation. This law says 
that bodies behave as if " every particle of matter " attracted 
" every other particle with a force that is proportional to the 
product of their masses and inversely proportional to the square 
of the distance between them." Treating bodies as particles, they 
may be considered as each at a point. The formula to express 

this law is F = k —— . That the law applies to bodies through- 

(JL 

out space was established by Newton's demonstration that the 
motion of the moon conformed to it; then it was extended to 
the entire solar system. Newton's great w*ork, then, in connec- 
tion with gravitation, was not the determining of the principle, 
but of its universality (Lodge, Pioneers of Science). That it 
applies to small terrestrial bodies under the influence of the earth 
has just been shown; that it applies to such small bodies in their 
action upon each other at short distances was first established 
experimentally by the famous " Cavendish experiment." This 
experiment, so named from Henry Cavendish who first (1797-98) 
successfully performed it, was designed by Rev. John Mitchell, 
but he died before he could try it. 



42 PROPERTIES OF MATTER; MECHANICS 

30. Gravitation Constant. — The fundamental formula ex- 
pressing the law of gravitative attraction is 

F = K?f. (A) 

In this, we can so choose our units of mass, distance and force 
that K shall be unity, and then in such units the force of gravita- 
tive attraction between masses would be 

^ mm' 

F = — — -• 



For instance, if we define as our unit of force the force which a 
unit mass exerts upon another unit mass at a unit distance, then 
in formula (A) F, m, m' and d are all unity at the same time, and, 
with that understanding, the equation makes K = 1. But such 
a unit force would be different from any in common use. 

Having in mechanics already defined our unit of mass, of 
distance and of time (and therefore of acceleration), the unit 
of force, as derived from its effect in producing acceleration, is of 
necessity the force which produces unit acceleration in unit mass. 
In the c.g.s. system we have already determined this to be the 
dyne, and we do not know this to be the gravitation unit above 
described. In fact, since the acceleration of a gram of matter, 
under the attraction of the whole earth (many grams), at a dis- 
tance of 4000 miles is 980 cm. /sec. 2 , and therefore the force equals 
980 dynes, it is probable that the attraction due to one gram is 
much less than a dyne even at as small a distance as one centi- 
meter; so our problem is to see what K in the above equation 
would be, to give the number of dynes in F, if m and m' are each 
one gram and d is one centimeter. With that determined, if 
we use that value of K, then the equation will always correctly 
give the force in dynes, due to the attraction of masses expressed 
in grams, at distances expressed in centimeters; and K, thus 
determined, is called the " gravitation constant." (It might also 
be determined for the f.p.s. system.) 

31. The Cavendish Experiment. — The apparatus, Fig. 11, 
consists of a delicate torsion suspension fiber w, a light arm a, 



THE CAVENDISH EXPERIMENT 



43 




at the ends of which are two equal small balls of known mass m. 
The angle a through which the fiber is twisted by a force of one 
dyne applied on each side of the suspension 
fiber in opposite directions at half a unit 
distance from the suspension, i.e., with unit 
distance between the forces, is measured. 
Then two equal large balls of mass m' are 
placed at a distance d (center from center) 
from the balls m, and the angle of twist 6, 
when the balls are at this distance, is ob- 
served. The observation is repeated with 
the balls m' changed to the opposite side of 
m. Whatever the two equal rotative forces applied at right 
angles to a, the twist is proportional to one force multiplied 
by the distance between the two; and various pairs of forces 
applied at m and m' will be proportional to the angles of twist 
which they produce. In the first case above, 

a = C (l).(l) (B) 

where c is a constant depending on the elastic quality of the 
suspension fiber. In the second case, 

6 = cfa. (C) 

Kmm f 



Fig. ii. 
Torsion Balance. 



But 



Then 



or 



J 


d? 


e 


Kmm' 

= c v a 


e 


Kamm' 


a 


d 2 


K 


d 2 e 




amm' a 



(D) 



(E) 



(F) 



Note. — Any two parallel equal forces in opposite directions are called a couple. 
The effect of a couple is solely to produce rotation, and the rotative effect, 
called the moment of the couple, is measured by the product of either force by the 
perpendicular distance between them. When this product is unity the couple is 
called a unit couple. In such an illustration as the present, the unit couple would 
be obtained in practice by using a couple consisting of any known equal forces 
(not necessarily unity), at any known distance apart, having a calculable moment 



44 PROPERTIES OF MATTER; MECHANICS 

and producing an observed twist. Then the twist for unit moment would be this 
observed twist divided by the moment of the couple producing it. The known 
force, then, need not be unity and might be applied at m. 

a and are determined by turning a milled head H until the 
twist produces the required force at m, i.e., holds m and m' apart 
the required distance d. Thus all the quantities in the second 
member of Eq. (F) are known, and K is determined. Since the 
time of Cavendish the experiment has been often repeated with 
great care, the best results up to this time giving for K in c.g.s. 
units the value 6.6579 X io~ 8 . It is thus seen that, as compared 
with magnetic or electric attractions or repulsions, gravitation 
is an extremely feeble force, although when acting between the 
enormous masses of the heavenly bodies it is sufficient to control 
their movements. 

32. Weighing the Earth. — If by weight we mean the force 
with which the earth attracts a body, then the weight of the 
earth itself is an indefinite expression; but usually the process 
of weighing is a comparison of the mass of a body with that of 
some standard body, and in this sense weighing the earth would 
be determining how many units of mass it contains. That being 
determined, if the volume also is known, then the ratio of the 
mass to the volume is its mean density. 

Since at the surface of the earth the attraction of the earth 
for one gram is g dynes, we have, calling mass of the earth M, 

K{i)M . 

a = — *-* . 

Substituting for R its value (3962 miles) in cms., for g its value in 
cm. /sec. 2 (981), and for K its value as above determined, we find 

M= 6272 X io 24 grams 
= 6272 X io 18 tonnes. 

(io 18 is a billion of billions.) 

In this sense Cavendish is said to have been the first to "weigh 
the earth." 

This mass in grams divided by the volume of the earth in cubic 
centimeters gives the number of grams per cubic centimeter 



CENTER OF GRAVITY 45 

in the earth. This is called the mean density of the earth and is 
5.5268 g./c.c. 

33. Center of Gravity. — Gravity acting on every particle 
of a body constitutes a system of parallel forces, the weight of 
the body being the resultant of these forces, which, in the case 
of parallel forces, is their sum. For any given body the resultant 
of these forces will always pass through one point, no matter 
what may be the position of the body. (Shown from principles 
of mechanics.) This point is called the center of gravity of the 
body, and may be outside of the material composing the body, as, 
for example, in a ring or hoop. Regarding the entire body in its 
mechanical relations to other bodies, it may be treated as if it 
were all at its center of gravity. Considered in its parts, each 
part may be regarded as concentrated at its own center of 
gravity. 

For stability of position, if a vertical line through the center 
of gravity passes outside of the line circumscribing the base on 




Fig. 12. Stable, Unstable and Indifferent Equilibrium. 

which the body stands, i.e., the circumscribing line with no re- 
entrant angle, the body will topple over or be unstable; but if 
the vertical passes within the base the position is stable. In the 
former case it is easily seen that a toppling of the body neces- 
sarily means a lowering of the center of gravity, and in the latter 
case a raising of it. The body is stable, therefore, when a move- 
ment of overturning raises the e.g., and unstable when such 
movement lowers the e.g. There is a third possibility, in which 
a turning neither raises nor lowers the e.g.; this position is called 
neutral or indifferent. The three conditions are illustrated in 
Fig. 12 by a cone on its base, its apex and its side, respectively. 



46 PROPERTIES OF MATTER; MECHANICS 

34. Potential Energy Tends to a Minimum. — When the 
parts of a body or of a system of bodies are in any degree free to 
adjust themselves under forces that exist within the system, they 
will always so rearrange themselves as to make the potential 
energy of the system as small as possible. From the last article 
we see that, treating a given body and the earth as a system, the 
potential energy is the greatest when the e.g. of the body is 
farthest from the earth; and, in accordance with this energy 
principle, a body will always so move under the action of gravity 
as to bring its e.g. to the lowest possible position. In doing this 
a body may apparently roll uphill, at least for a short distance. 

Experiment No. 11, page 91. Mechanical Paradox. — 

Loaded cylinder of wood; the e.g. being eccentric, the cylin- 
der rolls uphill a part of a revolution; also in the " mechanical 
paradox" the double cone apparently rolls up an inclined plane; 
also various toys. 

35. Mechanical Powers. — In machines the relation of the 
applied force P to the resistance W that is overcome is deter- 
mined by the principle that the energy acquired by the body 
moved equals the work done in moving it. If S p denote the 
distance moved by the point of application of the force, and S w 
the distance through which a weight W is raised or a resistance 
W is overcome in the direction of the resistance, 

FXS P = WXS W . (1) 

The first member of this equation represents the work done by 
the applied force, and the second member is an expression of the 
work against the resistance, and for equilibrium these two are 
equal. This part of the problem is mechanics. The equation 
can be applied, provided it is possible to determine what space 
will be traversed by the resistance when the point of application 
of the force moves over a given distance in the direction of the 
force. This depends on the arrangement of the mechanism, 
and this part of the problem is not mechanics but geometry. 
Therefore, examine the arrangement of the mechanism, and from 
the geometry of it determine the distance through which the re- 



MECHANICAL POWERS 47 

sistance is moved when the point to which the moving force is 
applied has moved a known distance. If free from friction, 
these forces will be to each other inversely as the distances. 

The principle may be illustrated with lever, straight or bent, 
with pulley, inclined plane, wheel and axle. 

If F is the force, parallel to an inclined plane of height h and 

length L, to just support a weight W, since 

Pv/ r TJ/ v/ 7 k F ma 
FXL = W Xh, -= — = — , 
L W mg 

where a is the acceleration with which W would freely descend 
the plane. This gives Galileo's mode of determining the value 
of g. 

Experiment No. 12, page 91, Determination of g. — 

With pulley on wire, if 

L = 950 cm., h = 95.6 cm., / = 4.4 sec. 

2 L 
Since L = \ at 2 , a = — - = 98.0, and from above equation g = 
t 2 

a — = 980, nearly. 
h 

The above relation also leads to the principle of virtual veloci- 
ties, a purely geometrical conception (but the basis of Lagrange's 
Analytical Mechanics). 

Illustrate with rolling-pin model; also differential windlass. 

Experiment No. 13, page 91, Rolling-pin Model. — 

If the earth and a weight on an inclined plane be regarded as 
a system, and the weight be drawn up the plane, work is done on 
the system (by external force) and the energy of gravitative sepa- 
ration is thus increased. The force F necessary for this does 
work by being exerted through a distance s to raise a weight W 
against gravity a height h, so that Fs = Wh. Observe that the 
potential energy of the system is now increased by the amount 
of work that has been done upon it, and the weight so raised will 
return to its former position if free to do so, or the potential 
energy tends to a minimum. (In such decrease of potential 
energy, what becomes of the energy?) 



48 PROPERTIES OF MATTER; MECHANICS 

Equation (i) above is applicable to every contrivance for rais- 
ing a weight. 

Examples. — 

i. The arms of a lever make a right angle at the fulcrum. What hori- 
zontal force applied to the vertical arm at 33 cm. from the fulcrum will 
support a weight of 10 kg. suspended from the horizontal arm at 10 cm. from 
the fulcrum? Ans. 3030 gm. 

2. If a boy weighing 90 pounds has a lever 5 ft. 5 in. long, how should 
he use the lever and his weight to raise a stone weighing 300 pounds? Sup- 
posing he can lift 100 lbs., show another way for him to place the bar so as 
to raise the stone. (Neglect the weight of the lever,') 

3 . In a hoisting apparatus the hand, pulling with a force of 20 pounds upon 
a rope, draws it 50 ft. in raising a weight a height of 4 ft. What is the weight? 

Ans. 250 pounds. 

4. The crank arm of a windlass is 50 cm. long, and the shaft, around 
which is wound a rope to draw up a weight, is 18 cm. in diameter. What 
force must be applied to the end of the crank to raise a weight of no kg.? 

Ans. 19.8 kg. 

5. If the roller R, Fig. 7,8, p. 87, weighs 120 g. and the diameters are 
2 cm. and 7 cm., what must be the weight of W to just sustain R? What 
weight would be required if the two diameters were equal? 

Ans. First, 48 g.; second, infinity. 

36. Rotation ; Moment of a Force. — If all parts of a body 
move in equal parallel paths it is said to have a motion of 
translation; the velocity or change of velocity is the same for 
every part of the body; but without the body as a whole chang- 
ing its locality, it may turn about some point or line as an 
axis. This is a motion of rotation. In it all parts of the 
body describe a definite portion of a complete circumference 
about the axis in the same time, although the parts far from the 
axis move in their respective paths faster than those near the 
axis. The parts have the same angular velocities, but their 
velocities in their circular paths, i.e., their linear velocities, 
are proportional to their distances from the axis. The angular 
velocity of the whole body is expressed by the same number 
as the linear velocity of a particle at one unit distance from 
the axis. If the axis is fixed, the body may have rotation, 
although it cannot have translation. 



ROTATION; MOMENT OF A FORCE 49 

To set a body in rotation or to change its rate of rotation 
requires force just as in linear motion, but the effectiveness of 
a force in producing rotation depends not only on the magnitude 
of the force, but also upon the distance from the axis of its 
line of direction. Every one knows that a given effort exerted 
at the rim of a wheel is more effective in turning the wheel 
than if applied near the axle. So the turning effect of a force is 
measured by the product of the force by the perpendicular 
distance from the axis to the line of the force. This distance is 
called the lever arm of the force, and this product is called 
the moment of the force. A force of 20 pounds acting at a 
distance of 5 inches from the axis, would have as great a turning 
effort as one of 100 pounds at one inch from the axis; and if 
these two forces were so directed as to tend to rotate the body 
in opposite directions, they would exactly counter-act each 
other, and the body would be in equilibrium so far as rotation 
is concerned. 

If a body is to be in complete equilibrium it must have no 
tendency to change of motion, either in translation or rota- 
tion. The latter is secured by having the moments of the forces 
tending to produce rotation in one direction equal to the moments 
of those tending to produce rotation in the opposite direction, 
no matter what point is chosen as an axis. 

Also if one force is truly a " resultant " of two or more 
other forces, it must be able to accomplish just what they could 
do, and therefore its moment must be equal the sum of their 
moments. 

This principle is readily applied to many of the problems 
already considered. Apply the principle of moments to Examples 
1, 2, and 4, in Article 35, neglecting the weight of the parts 
of the apparatus. 

37. Moment of Inertia; Energy of Rotation. — Let P be a particle in 
a body of any shape, Fig. 13, which is rotating about C under the action 
of forces applied at one or more points of the body. If the parts of the 
body are rigidly connected to one another, a force applied at any point 
is communicated to all parts of the body by internal action from particle 




50 PROPERTIES OF MATTER; MECHANICS 

to particle. Among these particles action and reaction are mutual, and 
if rotation is accelerated, the acceleration will be in obedience to just so 
much force on each particle as equals the mass of the particle multiplied 
by its acceleration in the line of its motion, i.e., the tangential direction. 
Let Wi = the mass of a particle, n its distance from the axis of rotation, 
a the angular acceleration, which is alike for all particles. Its linear 
acceleration is na, and the force upon the particle in the direction tan- 
gential to the circular path in which it is moving is Wifia. The moment 
of this force is Wi 2 a; similarly for any other 
particle of mass m 2 at distance r 2 , the moment 
of the effective force on it is nhr 2 2 a, and for all 
the particles the total moment of the tangential 
forces is ^mr 2 a, where 2 simply stands for the sum 
of all the like quantities; or since a is a common 
factor multiplying each mr 2 , it may be written 
aZmr' 1 . The sum Swr 2 is called the moment of 

_. inertia of the body with reference to the axis C. 

rig. 13. 

Suppose the acceleration of the body is due 

to a single force F, whose direction is along a line AO, passing at a dis- 
tance CD = p from the axis C. The force may be regarded as applied at 
any point in its line of action as, say, at 0, and its effect upon the speed 
of rotation is measured by its moment Fp. Then we should have Fp = 
aZmr 2 . If, instead of a single force, there are various forces F, each at 
its own distance p from the axis, the total moment of rotating forces is 
xFp, and this will equal the total moment of effective forces on the 
particles, or 2Fp = aXmr 2 . That is, the sum of the moments of the applied 
forces is equal to the angular acceleration they produce, multiplied by the 
moment of inertia of the body. This is one of the most important prin- 
ciples in the dynamics of rotation. 

Determining how much the moment of inertia of a body 
amounts to is a mathematical process with no regard to physics. 
The mass of every element of the body is multiplied by the 
square of its distance from the axis, and these products are 
added together. There can be a definite distance from the par- 
ticle to the axis only if the particle is infinitely small, so the process 
of exact computation is essentially one of infinitesimal calculus. 

The idea of moment of inertia is applied to geometric figures, 
whether plane or solid, by using the area or volume instead of 
the mass. 



ENERGY OF ROTATION; FRICTION 51 

For a body of definite mass and figure it is evident that the 
moment of inertia will depend upon the position of the axis with 
reference to which the moment is computed, — in a rotating body, 
the axis of rotation. In a plane figure the axis may be a point 
or a line in the surface; in a solid the axis of rotation is a straight 
line, and in advanced dynamics it is shown that the moment of 
inertia is less for an axis through the center of gravity than for 
any other axis in the same position, i.e., parallel to it. 

If to = the angular velocity of the body, riw = linear velocity of Wi, 
and as the kinetic energy of a body is the product of one-half the mass 
by the square of its linear velocity (p. 30), \m\r\ t m' 1 = the kinetic energy 
of mi, and since w is alike for all the particles, the total energy of rotation, 
the sum of energy of all the particles, is |o 2 2w 2 ; or one-half of the prod- 
uct of the square of the angular velocity by the moment of inertia of the 
body. If a mass of as many units as the Xmr 2 were all concentrated at a 
distance of one unit from the axis its moment of inertia would be the same 
number as its mass and if it rotated with the same number of turns per 
second as the body it would have the same energy of rotation. That is 
the physical significance of the moment of inertia of a rotating body. 

A rotating body of given mass will have greater moment of inertia and 
consequently greater energy of rotation for a given speed, the farther its 
material is from the axis. A flywheel of small weight, if the material is 
mostly in the rim, would have more energy than a heavier one of the same 
diameter if concentrated in or near the hub. So a flywheel of an engine, 
whose purpose is to steady the action of the mechanism, is constructed on 
that principle, and if the driving effort of the steam is variable, or applied 
by means of a crank, so that at points it is contributing nothing to turn 
the wheel, the flywheel gives up some of its energy to carry the rotation past 
the " dead centers " with little change of speed, and if the motive power 
of the engine were cut off entirely the flywheel would keep up the motion 
until as much additional work was done as equalled its energy of rotation. 

38. Friction. — The relation of force and resistance in ele- 
mentary machines, as presented in the preceding article, is on 
the assumption that the entire work is expended in overcoming 
the final single resistance. In fact, some of it is expended in 
overcoming intermediate prejudicial resistance causing a waste 
of work. The chief of such resistances is friction. Its investi- 
gation must be left to closer study of mechanics, but while we 



52 



PROPERTIES OF MATTER; MECHANICS 



usually think of friction as something undesirable and therefore 
to be got rid of, we must not overlook its advantages, which are 
simply inestimable. 

Example from Watson's Physics, Ex. g of Chap. X. — " A kilogram weight 
sliding down an inclined plane 9 cm. high reaches the bottom with a velocity 
of 5 cm. per second. How much energy has been rubbed out of it during 
the descent (g = 980)?" 

Mass M = 1000; g = 980; h = 9 cm. Potential energy of M at top of 
plane = Mgh = 8,820,000 ergs. At foot of plane, v = 5 cm. /sec. ; kinetic 
energy = \ Mv 2 = 12,500 ergs. Loss by friction is the difference, or 
8,820,000 — 12,500 = 8,807,500 ergs. 

39. Properties of Matter. — Besides those properties which 
attach to bodies as a whole, sometimes called molar properties, 
and which are commonly the subject of mechanics, physics is 
concerned with others called molecular properties, which repre- 
sent conditions due to the structure of matter. These are chiefly 
such as to indicate internal forces in the body. 

That matter is discrete is indicated by its porosity. This 
is exemplified by its compressibility or expansibility. Either 
of these qualities alone would not demonstrate 
porosity, for we might conceive of its being due 
to a shrinking or an enlargement of the particles 
themselves; but when an intimate mixture of 
two substances is attended by a diminution of 
volume, the inference is greatly strengthened that 
such a rearrangement of the molecules has taken 
place as to bring them closer to one another- 
This may be shown by carefully pouring upon 
water an equal volume of alcohol, as in Fig. 14, 
and then mixing the two liquids. If the two 
liquids fill the vessel to the mark A, after mix- 
ing they will only rise to a point B, showing a 
contraction in volume of about three per cent. 
Similar contraction occurs with other liquids, 
^ion of Lkmids P° ros ^y is also indicated by the amalgamation 
on Mixing. of gold or other metals with mercury. 




Water 



FLUID PRESSURE $3 

One of the chief effects of the interaction between molecules 
is elasticity, and this accounts for a good many phenomena in 
physics. The law of elasticity, known as Hooke's law (ut tensio 
sic vis) , is that the force of distortion is proportional to the distor- 
tion; or, briefly, stress is proportional to strain. 

Since, then, when a particle of an elastic body is displaced the 
force tending to restore it to its first position is directly pro- 
portional to the displacement of the particle, a body or particle 
moving under elastic reaction will have S.H.M. All vibrations, 
then, that are due to elasticity are S.H.M. They include nearly 
all the phenomena of sound and sounding bodies. (Refer to 
Maxwell, Matter and Motion, pp. 122-125.) 

40. Fluids. — Some phenomena characterize fluids generally, 
others are peculiar to liquids or to gases separately. 

Mechanics of liquids in general is hydrodynamics; of liquids at 
rest, hydrostatics; of liquids in motion, hydrokinetics or hydraulics. 

41. Pascal's Principle. — Fluids transmit (not necessarily 
exert) pressure equally in all directions. This might be inferred 
from the mobility of a fluid. The principle is useful for multi- 
plication of force, as in a hydrostatic press. 

Pressure of a fluid at rest is normal to the surface pressed; 
otherwise, if resultant pressure were oblique, by reason of the 
perfect mobility of a fluid the particles pressed obliquely would 
move along the surface and the fluid would not be at rest. 

Since the ocean surface is not that of a sphere, normals to the 
"level " ocean surface do not pass through the center of the earth. 
As a consequence of the freedom of movement of the particles 
of a fluid, it cannot have shearing elasticity, but only volume 
elasticity. Of fluids, only liquids have a "free surface." (See 
definition of liquid and gas, Art. 14.) 

42. Pressure of a Liquid Due to Weight. — Under gravity, the 
pressure of a liquid is proportional to the depth below the 
free surface. Also, the pressure upon any submerged surface equals 
the weight of a column of the liquid whose base is the area pressed, 
and whose height is the distance from the center of gravity of the area 
to the jree surface of the liquid. Thus, in a cubical vessel filled 




54 PROPERTIES OF MATTER; MECHANICS 

with liquid, the pressure on each side is one-half the weight of 
the contents of the vessel, and the total pressure on the sides and 
bottom equals three times the weight of the liquid. A tall but 
very narrow column of liquid will suffice to burst a strong cask, 
though only a small quantity of the liquid is needed to fill a tube 
containing such a column to a considerable height. 

43. Center of Pressure. — This is a point of a surface under 
pressure at which the total pressure on the surface might be 

regarded as concentrated. 
It is then a point at which 
an equal opposite pressure 
would maintain the surface 
in equilibrium. If AB, Fig. 
15, represents a strip (or line) 
as a vertical element in the 
side of a vessel under pres- 
sure from the liquid of depth 
Fig. 15. Center of Pressure. ABj and D j s the center of 

pressure, then a contrary pressure R at D equal to the total out- 
ward pressure on AB will exactly counterbalance that outward 
pressure. 

The center of pressure is always below the center of gravity of 
the surface pressed unless the latter is horizontal, in which case 
all its points are at the same depth below the surface of the liquid. 
For a strip of uniform width, as AB, since the pressure is pro- 
portional to the depth, if p is the pressure at the depth unity, 
then at any depth d the pressure is pd, and may be represented 
by the arrowheaded lines which increase in length uniformly 
from A to B. The bounding line AC is a straight line of uniform 
slope, and the total pressure against AB would be represented 
by the sum of all the pressure lines from A to B, i.e., by the area 
of the triangle ABC. If the triangle were laid upon AB as a base 
and its weight were equal to the total pressure of the liquid, then 
the base AB of the triangle would have the pressure distributed 
upon it just as the pressure of the liquid is distributed upon the 
vertical face AB. But the weight of this triangle as a whole may 



A LIQUID AT REST 



55 



be considered as acting at the center of gravity of the triangle, 
which is two-thirds of the distance from A to B, or the center of 
pressure on A B is at two- thirds of the depth of the liquid. The 
e.g. of the filament AB is at one-half the depth AB. 

Note. — The center of pressure, in statics, corresponds to the center of percus- 
sion in dynamics. The determination of this point belongs to higher mechanics, 
but it may be located in this wise. 

Regarding the portion of the surface under pressure as a detached plane surface 
suspended from the line of its intersection with the upper surface of the liquid, and 




Fig. 1 6. Center of Pressure and of Percussion. 

oscillating about that line as an axis, the vertical distance from the axis to the center 
of pressure is equal to the length of the simple pendulum oscillating in the same 
period with it. If the surface were the triangle ABC, in Fig. 16, (a) and (b), in 
the first the center of pressure D is at one-half the depth of the liquid, and in the 
second case, at three-fourths the depth. The center of percussion is a point at 
which a blow would produce no shock upon the axis of suspension. (The distance 
from the axis of suspension to the center of percussion or the center of pressure 
equals the moment of inertia of the surface divided by the moment of the surface.) 

Examples. — 

i. A hole 20 cm. square is made in the vertical side of a ship, the upper 
edge of the hole being 2 meters below the surface of the water. What force 
must be exerted to keep the water out by holding a board against the hole, 
supposing one cubic centimeter of sea water to weigh 1.025 grams (Art. 42). 

Ans. 86+ kg. 

2. If (a) and (b), Fig. 16, are prismatic vessels of the same dimensions, 
filled with the same kind of liquid, how does the pressure against the end 
of one vessel compare with that against the end of the other? 

Ans. Twice as great in (b) as in (a). 

44. A Liquid at Rest in Communicating Vessels. — From 
Art. 42 it is seen that any number and variety in shapes of 
vessels containing a given liquid, and having the same size of 



56 PROPERTIES OF MATTER; MECHANICS 

base, will have the same pressure on that base if the liquid is at 
the same height above the base; and if all are in communication 
with one another by any variety of size in the opening from one 
to another, the liquid will rise to the same height in all to come 
to equilibrium; for wherever any one connects with any other 
the surface of union is a common area to both, and will be equally 
pressed by the liquid in both only when there is an equal height 
of liquid above it on both sides. 

Illustrate with various-shaped vessels, also with apparatus, to 
show equal pressure in all directions, laterally and vertically. 

45. Archimedes' Principle. — A body wholly or in part 
immersed in a fluid loses a part of its weight equal to the weight 
of the fluid displaced. This statement, known as the principle 
of Archimedes, may be so extended as to apply to the case where 
the loss of weight is greater than the weight of the body, in which 
case the weight remaining to the body is a negative quantity, 
or a force greater than its own weight is required to keep the 
body submerged. This loss of weight is the buoyant effort of 
the fluid upon the body. If the body weighs more than its own 
bulk of the fluid, it will sink through the fluid under the action of 
gravity, but with diminished weight; if it weighs less than its 
bulk of the fluid, it will sink into the fluid until it has displaced 
as much fluid as has a weight equal to that of the body. The 
principle was originally applied only to solid bodies immersed in 
liquids, but it holds equally for all fluids, gases as well as liquids. 
(Hence the difference between the weight of a body in air and 
in a vacuum.) 

Demonstrate for liquid by the hydrostatic balance with the 
cup and cylinder; also by the Cartesian divers. 

Experiments Nos. 14 and 75, pages 92-94. — Demonstration and Illustra- 
tions of Archimedes' Principle. 

46. Buoyancy. — This term expresses the resultant of the forces 
tending to sink a body in a liquid and those supporting it, and 
means that the total upward pressure upon the body may be more 
(or less) than the total downward pressure and weight combined, 

A body such as wood or cork rises through and floats upon 



BUOYANCY 



57 




Fig. 1 7. Pressure upon a 
Submerged Body. 



water because, we often say, it is specifically lighter than water, 
and correspondingly we say that iron sinks because it is heavier ; 
but a floating body if submerged will rise, not because it is 
specifically lighter than the liquid, but because of the vertical 

upward pressure acting upon it. That , r 

such pressure should be greater upward 
than downward is owing sometimes, it is 
true, to the less specific gravity of the 
body, but it is that pressure that causes the 
body to rise. In Fig. 17 the body C is 
pressed downward by the weight of a 
column of liquid of height EF plus the 
weight of C, and is pressed upward by the 
weight of a column of the liquid of the 
height GF. If C be pressed upon the bot- 
tom of the vessel so as to exclude the liquid 
from beneath it, it cannot rise, no matter how light the body 
nor how heavy the liquid; it is the more securely fixed to the 
bottom the greater the sp. gr. of the liquid. 

Experiment No. 16, page 94. — Cork Remains Submerged under Mercury. 

The body, then, comes to the surface by reason of the upward 
pressure under it. (Swimming is no easier in very deep than 
in moderately deep water.) Ordinarily, in such discussions, the 
part played by the pressure of the air is not considered, as it 
usually counteracts itself, aiding the upward pressure of the 
liquid as well as pressing the body down. If such condition does 
not exist, if the air pressure acts only in one direction, the con- 
ditions of equilibrium would require that this be taken into 
account; and, to generalize the statement of the conditions of 
buoyancy, we would say: " A floating body sinks to a depth such 
that the buoyant effort which the liquid exerts upon it is greater 
than the pressure which the air exerts upon it from above down- 
wards, by an amount equal to the weight of the body." 

Now let us conceive of a vessel containing a liquid, and that a 
body fitting the vessel air-tight is placed upon the liquid. There 
is then air pressure upon the body from above, there is the weight 



58 PROPERTIES OF MATTER; MECHANICS 

of the body, and there is liquid pressure from below, and if it 
is a floating body, the preceding statement exactly applies. 
Suppose the relative positions of the vessel, liquid and float to 
remain the same with the vessel inverted; then the proposition 
would read conversely: " The pressure which the air exerts upon 
the body from below upwards is greater than the pressure which 
the fluid exerts upon it from above downwards, by an amount 
equal to the weight of the body, and equilibrium results. In 
case the upward pressure is still greater, the body rises." 

Experiment No. 17, page 94. — One Test Tube Falling Upwards into 
Another. 

47. Specific Gravity. — This is a term to be applied to sub- 
stances, not to bodies; for two bodies of the same material 
may differ in gravity, which is weight, but be alike in specific 
gravity. Whenever the term " specific " is applied to a quality, 
it means the measure of that quality in one kind of material as 
compared with the measure of it in a specified quantity of some 
specified substance taken as a standard. In physics, the sub- 
stance oftenest used as a standard is water, and "specific gravity" 
of a substance means the weight of any portion of such substance 
compared with the weight of an equal volume of water. Its nu- 
merical value is the ratio of the weight of the substance to the 
weight of an equal volume of water, and therefore it is an 
abstract number. Obviously the size of the body used in the 
comparison makes no difference, since it is to be compared with 
a body of water of the same size. (See Barker, p. 162.) 

Archimedes' principle is the basis of the methods of determin- 
ing specific gravity by weighing, for if a body is weighed in air 
and then in water, the loss of weight in water is the weight of an 
equal volume of water, and therefore the specific gravity is the 
weight in air divided by the loss of weight in water. 

c wt. in air /A s 

Sp. gr. = ; (A) 

loss of wt. in water 

If we take as unit weight the weight of unit volume of water, as, 
e.g., one gram is weight of one c.c. of water, then the loss of 
weight in water is at once the weight (in grams) of its volume of 



SOLUTION OF THE PROBLEM OF HIERO'S CROWN 59 

water and also the number of units of volume (c.c.) in the body, 

and the specific gravity then may be the ratio of the weight to 

the volume, or from (A), 

wt. in grams , , . wt. in grams /T ^^ 

sp. gr. = —7-^ ~ and vol. m c.c. = (-B) 

vol. in c.c. sp. gr. 

48. The Celebrated Story of " Eureka." — The following account of 
Archimedes' discovery of his "principle" is quoted by Mach (Science of 
Mechanics, pp. 86, 87), from Vitruvius, De Architectura. 

"Hiero, when he obtained the regal power in Syracuse, having, on the 
fortunate turn in his affairs, decreed a votive crown of gold to be placed in a 
certain temple to the immortal gods, commanded it to be made of great 
value, and assigned for this purpose an appropriate weight of the metal to 
the manufacturer. The latter, in due time, presented the work to the king, 
beautifully wrought; and the weight appeared to correspond with that of 
the gold which had been assigned for it. 

"But a report having been circulated that some of the gold had been 
abstracted, and that the deficiency thus caused had been supplied by silver, 
Hiero was indignant at the fraud, and, unacquainted with the method by 
which the theft might be detected, requested Archimedes would undertake 
to give it his attention. Charged with this commission, he by chance went 
to a bath, and, on jumping into the tub, perceived that just in the proportion 
that his body became immersed, in the same proportion the water ran out 
of the vessel. Whence, catching at the method to be adopted for the solu- 
tion of the proposition, he immediately followed it up, leapt out of the vessel 
in joy, and, returning home naked, cried out with a loud voice that he had 
found that of which he was in search, for he continued exclaiming, in Greek, 
evprjKa, evprjKa (I have found it! I have found it!)." 

49. Solution of the Problem of Hiero's Crown. — The method by which 
the principle was applied in this famous case is shown in the following ex- 
ample (from Goodeve's Mechanics) : 

"The crown of Hiero, with equal weights of gold and silver, were all 
weighed in water. The crown lost t? of its weight, the gold lost yV of its 
weight, and the silver lost A of its weight. Prove that the gold and silver 
were mixed in the proportion of 11 : 9." 

If - = the part of the crown's weight that was gold, then = the 

x x 

part of the weight that was silver, and the ratio of gold to silver is — - — . 

x — 1 
Let w = the weight of the crown. 

If any weight of gold loses 7? when weighed in water, its specific gravity 

is weight in air divided by loss of weight in water, or -V, and from equation 

(B), Art. 47, the volume of any quantity of gold will be wt. -5- sp. gr. 



60 PROPERTIES OF MATTER; MECHANICS 

Weight of gold in the crown is - w. and - — = volume of gold in crown. 

x 77 x 

2 (X — i) I 

Similarly, — * w = volume of silver in crown, and — • w = volume 

21 x 14 

of the crown itself. Equating the sum of the volumes of the two metals 
with the volume of the crown itself, 

! 4 w , 2 (x — 1) w _ 1 

i — w. 

77 x 21 x 14 

This equation gives x = — • 
n 

Then - is — which is the gold, and — is the silver, or the gold is to the 

x 20 20 

silver as 11 : 0, Q.E.D. Also, the above ratio = — Q.E.D. 

x — 1 9 

A similar method may be applied to the determination of the respective 
weights of gold and quartz in a nugget containing the two substances. 

Examples. — (The buoyant effect of the air is neglected.) 

1. A piece of cork of mass 300 g. and sp. gr. 0.25 is placed in a vessel full 
of water. How much water will overflow? How much would overflow if 
the float were a piece of wood of the same mass as the cork, and sp. gr. 0.92? 

Ans. 300 c.c. 

2. A body weighs 62 g. in air and 42 g. in water. What is its specific 
gravity? What its volume? Ans. 3.1; 20 c.c. 

3. The sp. gr. of ice is 0.918 and that of sea water 1.03. What is the 
volume of an iceberg which floats with 600 cubic meters exposed? 

Ans. 5518 cubic meters. 

4. A solid which weighs 120 g. in air weighs 90 g. in water, and 78 g. in a 
solution of zinc sulphate. What is the sp. gr. of the solid and of the solution? 

Ans. 4; 1.4. 

5. A bottle weighs 25 g. when empty, 64.74 g. when filled with water, 
and 65.53 g- when filled with milk. What is the sp. gr. of the milk? 

Ans. 1.02. 

If a piece of rock of weight W consists of gold and quartz, let x and y be 
the weights of gold and quartz respectively, m, n, r } the sp. grs. of gold, 
quartz and the mixture. Then 

W = x + y. (1) 

Also, volume of specimen = vol. of gold + vol. of quartz, or, from Art. 47, 

^ = ^ + 2, w 

r m n 
and from Eqs. (1) and (2) the values of x and y may be determined. 



DENSITY 6l 

6. A diamond ring weighs 65 grains in air and 60 grains in water; find the 
weight of the diamond if the sp. gr. of gold is 17.5 and that of diamond 3.5. 

Ans. 5.625 grains. 

7. The sp. gr. of milk is 1.02. A quantity adulterated with water is 
found to have a sp. gr. of 1.015. What proportion of water has been used? 
(Suggestion: 1 c.c. of the mixture weighs 1.015 g., 1 c.c. of water weighs 
1 g.) Ans. Volume of water equals one-third of the volume of milk. 

50. Density. — This term, like specific gravity, is to be used not 
so much to distinguish one body from another as to distinguish 
the kinds of material of which the bodies are composed. It is the 
relation of the mass of a body to its volume, and would, therefore, 
be the same for all bodies of the same material, whatever their size. 

When so used, density must be expressed as so many units of 
mass per unit volume ; e.g. , grams per cubic centimeter, or pounds 
per cubic foot, etc. ; and the number thus obtained is called the 
absolute density of the substance. 

Absolute density of any substance, then, may have different 
numerical values according to the units in which it is expressed. 

When density is expressed in comparison with that of some 
particular substance taken as a standard, the number expressing 
it is an abstract number, and this is called the specific density of 
the substance. 

The specific density of any substance, then, may have differ- 
ent numerical values according to the substance that is chosen as a 
standard. If the standard substance have unit mass in unit 
volume, the specific density will be numerically the same as the 
absolute density. This is the case with water measured in c.g.s. 
units, for a mass of one gram of water at its maximum density 
has a volume of one cubic centimeter. 

The mass of any body in grams divided by its volume in cubic 
centimeters is its absolute density in grams per cubic centimeter, 
and the numerical value of this ratio is the specific density, com- 
pared with water. 

In physical comparison of densities water is usually taken as 
the standard, but sometimes gases are compared with air, or, more 
frequently, with hydrogen as a standard. Then the absolute 
density might still be expressed as gms./c.c, while the specific 



62 PROPERTIES OF MATTER; MECHANICS 

density would be a different number. For example, the absolute 
density of air would be 0.001293 g./c.c, and if hydrogen were the 
standard for comparison the specific density would be 14.43, but 
if water were the standard the specific density would be 0.001293. 

Since the weight of any body is directly proportional to the 
mass of it, the weight per unit volume of various substances will 
be in the same proportion as the mass per unit volume of the 
same substances. 

The ratio of the weight of, say, one cubic centimeter of a sub- 
stance to that of the same volume of water is its specific gravity. 
The ratio of the mass of one cubic centimeter of a substance to 
that of one cubic centimeter of water is its specific density; and 
this ratio is the same for masses and for weights ; therefore, when 
the same substance is chosen as the standard for specific gravities 
and for specific densities, the specific gravity of a substance and 
its specific density are the same number, and if the standard 
substance is water, the specific gravity, the specific density, and 
the absolute density in grams per cubic centimeter will all be the 
same number. 

Note. — Density should not be denned as the closeness of particles in a substance. 
While it is true that if a given mass of a substance, say, air, for example, have its 
particles closer (under compression) at one time than at another, it will be denser, 
it does not follow that of two unequally dense substances the particles of the denser 
one are closer together than those of the rarer. Especially is this noticeable with 
gases, in which, as will be shown (Arts. 77, 78), hydrogen, containing the same 
number of molecules in a given volume as oxygen, is only about one-sixteenth as 
dense. 

51. Determination of Density. — Any contrivance to find the 
number of grams in a cubic centimeter of a substance will deter- 
mine its density, and any contrivance to compare the weight 
of a body with the weight of an equal volume of water will deter- 
mine the specific gravity of the material of the body. This is 
with the understanding that water is the standard for densities 
as well as for specific gravity, so that the same number expresses 
the specific gravity and the specific density. - 

The forms of apparatus and the methods of using them are 
various, the following being the principal ones: 



DETERMINATION OF DENSITY 



63 



(a) The hydrostatic balance. 

(b) Hydrometer, constant immersion. 

(c) Hydrometer, constant weight. 

(d) Mohr's (or Westphal) balance. 

(e) Jolly's balance. 

(/") Specific-gravity bottle (pycnometer). 

(g) Volumometer (stereometer) (can be explained only after 

Boyle's law, and barometer). 
(h) Hare's apparatus. 

(Any convenient selection of these may be used 
for illustrating the lectures.) The principle of 
the last-named needs explaining. 

In any column of liquid the downward unit 
pressure under gravity varies as the height, or 
p oc h; also for a given height of column, the 
pressure varies as the density, or p oc 5 (den- 
sity) ; therefore, in general, p oc dh. In the 
apparatus, Fig. 18, the pressure due to each 
column is equal, being that of the atmosphere 
minus the pressure of the air in the common 
space above the two liquids. Therefore, calling 
the pressure, density and height p, 8 and h 
respectively, pi = kdihi, p 2 = kb 2 lh\ but pi = p 2 , 
therefore, 8ihi = 8 2 h 2 , or 




h 



Q.E.D. 



For further consideration of specific gravity Fig. 18. Compari- 
and density, see Lodge, Elementary Mechanics, son of Densities by 
Arts. 182 to 187; and Glazebrook and Shaw, iqm oumns - 
Practical Physics. (Alcoholometers, lactometers, etc., are only 
specially graduated forms of hydrometers.) 

Experiments Nos. 18 and 19, page 95. Specific Gravity and Densities. 

Examples. — 

1. A solid iron cylinder 5 cm. in diameter and 10 cm. long has a mass 
of 1 S^-S g- What is its density? Ans. 7.8 g. per c.c. 



64 PROPERTIES OF MATTER; MECHANICS 

2. If the specific density of mercury is 13.6, how many grams will be 
required to fill a tube 76 cm. long and 4 mm. in internal diameter? 

Ans. 129.9 g. 

3. The volume of a balloon filled with coal gas is 1000 cubic meters, and 
its weight 400 kg. If the density of the gas is 0.0007 g- P er cc - and that of 
the air 0.001293 g- P er c - c -> what additional weight can the balloon sustain 
in the air? Ans. 193 kg. 

4. In Hare's apparatus, Fig. 18, a solution of zinc sulphate stands in one 
tube at a height of 43 cm., while the level of the water in the other tube is at 
a height of 60.2 cm. What is the specific density of the solution? What 
its absolute density? Ans. 1.4; 1.4 g. per c.c. 

52. Surface Tension. — Up to this point, solids, liquids and 
gases have been considered in mass (molar physics); certain 
features, however, especially of liquids and gases, must be re- 
garded in their intermolecular actions (molecular physics) . 

The action of molecular forces is more easily examined in fluids 
than in solids. The form of a liquid which is separated from 
adjacent surfaces by force between its molecules is globular. In 
a small quantity of the liquid the molecular attraction is largely 
in excess of the effect of gravity, and the body is almost strictly 
spherical, — perfectly so, if it is in rotation about various axes. 
But when the mass is large it becomes flattened into a spheroidal 
form under the influence of gravity. The direct effect of molecu- 
lar attraction (cohesion) in such a liquid is to put the surface 
layer in a state of tension. This will bring the liquid mass into 
such a form as to include the mass with the least extent of surface 
possible; i.e., the potential energy of the surface film will come 
to a minimum. 

Experiments N os. 20 and 21, page 95. — Surface Tension. 

It may be shown that the energy of a particle of a fluid is 
greater when the particle is very close to the surface of that fluid 
( T oVo mr n-) than when it is at a greater distance from the sur- 
face. An effect of this is that the particles near the surface are 
drawn inward toward the mass of their own fluid, and the surface 
is put into a state of tension, called " superficial tension." The 
energy of the molecules constituting the surface layer, due to the 
action of molecular forces, is superficial energy, and it is upon this 



SURFACE TENSION 65 

energy that capillary phenomena depend. Superficial tension, or 
the tension in a film, whether single or double, is seen in the con- 
tractile force exerted by a soap bubble, and the measure of the 
surface tension is the force per centimeter exerted by the film 
across a line in the surface. 

Superficial energy depends upon the nature of both media of 
which the surface is a boundary. The media must be such as do 
not mix or we should have diffusion, but there is a coefficient of 
superficial energy for every surface separating two liquids that 
do not mix, a liquid and a gas, a gas and a solid, or two solids — 
none for two gases as any two gases diffuse into each other. 

Suppose we have a glass beaker partially filled with water. We 
then have the three media — glass, water and air — meeting along 
the circular line around the glass. Denote the tension of the 
surface separating the glass and water by T w , of that between 
glass and air by T a °, and that between air and water by T w a . 
These three tensions must be in equilibrium along the common 
line of junction, and therefore may comprise a triangle of forces. 
Furthermore, the angular positions of these surfaces, relatively 
to each other, will depend only upon the superficial tensions 
separating them, and therefore will always be the same for the 
same substances. 

But it is not always possible to construct a triangle of three 
given lines. One must not be greater than the sum or less than 
the difference of the other two, and so not every three sub- 
stances will take a position of equilibrium with distinct surfaces of 
separation. For example, if the tension of the surface separating 
air and water is greater than the sum of the tensions between 
air and oil, and oil and water, then a drop of oil on water will 
not come into equilibrium but will spread out, inserting itself 
continually between the more urgently separated fluids, and 
following the shrinking surface of separation between water 
and air, the oil getting thinner indefinitely. 

When the superficial tension of a liquid is given, it is always 
understood that the liquid is in contact with air as the other 
medium, unless stated otherwise. 



66 



PROPERTIES OF MATTER: MECHANICS 



Suppose a horizontal surface of a solid, as glass, is in contact 
with two fluids, /i and/ 2 ; if the tension of the surface separating 
the solid from the first fluid is greater than the sum of the ten- 
sions between glass and/ 2 and between /i and/ 2 , the first fluid, f h 
will gather into a drop, and / 2 will spread over both /i and the 
solid (glass). If one of the fluids is air (usual case), and the 
other is a liquid, then the liquid, if it corresponds to/i, will gather 
into drops. This would be the case with mercury; but if the 
liquid corresponds to/ 2 , it will spread over (i.e., wet) the surface 
of the glass; this would be the case with water. 

If the above inequality does not apply, the tension of the 
surface separating two of the substances is greater than the 



nB 




Water 



(a) 



A 



Fig. io. 



Air 




Mercury 



(6) 

Surface Tension. 



VA 



difference of the other two tensions. Suppose, for illustration, 
in the vessel before us (a beaker partly filled with liquid), 
T w a > Tj — 7V 7 . The side of the vessel being vertical, the 
tension between the glass and each fluid will be vertical. Sup- 
pose O, Fig. 19 (a) , represents the upper edge of the liquid. Let 
OB = 7V, OA = Tj, and OP = T w \ Make OQ = Tj - T a »; 
then, whatever be the value of the tension between air and water 
(= OP), P cannot be higher or lower from than Q, and, the 
tension being greater than OQ, takes a position like OP, the sur- 



CAPILLARITY 67 

face of the liquid making an angle with that of the solid, POQ, 
which is called the " angle of capillarity " a. (In fact, with water 
and glass, a = o, and the liquid film is spherical.) In cases 
where the resultant of the three tensions acts downwards, the 
liquid is depressed instead of elevated as in the case of mercury 
in glass, where a = 45 ±, Fig. 19 (b). 

Note. — The film, being in a state of stress, possesses potential energy, and its 
tendency at any point is so to readjust itself as to reduce this energy to a minimum. 
It will therefore contract to its smallest possible area. If it incloses a given volume 
of substance, the form of least surface is a sphere. 

As to the pressure of the film upon the figure which it incloses, if it has a curved 
surface, the normal pressure, due to tension T along a line of section whose radius 

of curvature is R, is proportional to - , and if R' is the radius of curvature of a sec- 

K 

tion perpendicular to the first, the pressure per unit of area at their intersection is 

IT 2 

as 75 "I" d> • I Q a sphere R = R', and the pressure is proportional to — . The sum of 
R R R 

— + w> represents actually the difference of pressure on the two sides of the film, 
R R 

and the film will always take a form such that at any point -5 + 17, shall be a mini- 

R R 

mum. If the film has the same pressure on both sides, as, e.g., a soap film on a 

wire frame and exposed to atmospheric pressure on both sides, then — + -^7 must 

R R 

equal zero; and if one radius is positive, the other is negative; if the surface is 

warped in shape, then at any point where the curve of section is concave along one 

line there must be, along a direction at right angles to this line, an equal curvature 

in the opposite sense, or convex. If the figure is plane, R and R' are both infinite. 

Water has a greater surface tension than any other liquid 
except mercury. It decreases rapidly with rise of temperature, 
and is much lessened by impurities. 

Experiments Nos. 22 to 24, page 96. — Surface Tension. 

53. Capillarity. — When a tube of fine bore, open at both 
ends, is dipped into a liquid, the surface tension not only raises 
or depresses the liquid in contact with the material of the tube 
on the outside, but may raise or depress the column of liquid 
inside the tube to a considerable distance as measured from the 
general level of the liquid at a distance of a centimeter or more 
from the tube. The action on the liquid in the tube is known as 
capillarity. It is due to surface tension and applies also to a 



6S 



PROPERTIES OF MATTER; MECHANICS 



liquid between two plates. If, in Fig. 20 (1), b is the distance 
between the plates, h (= BC) the height which the liquid rises 
above the outside level, and / the length of the prism thus lifted, 
the volume thus supported is bhl; if w is the weight per unit 
volume, the total weight is wbhl. This liquid is drawn up by 
the tension of the surface film along the glass. If the tension is 




(2) 
Fig. 20. Elevation or Depression of Liquids by Capillarity. 

T dynes per centimeter of its length, and the liquid joins the 
glass at an angle a, the vertical component of the force would be 
T cos a dynes per centimeter. In the case of water, a = o, and 
the lifting force is T dynes/cm. As there is such a line along 
each plate, the total lifting force is 2 Tl. Equating this with the 
weight supported, we have 2 Tl = wbhl, 

(A) 



whence, 



h = 



wb 



T and w should be expressed in like units. If T is dynes, and 
w is grams, the latter must be multiplied by 980. If, instead of 
plates, a tube of inner radius r (Fig. 20 (2)) be put into the liquid, 
the length of film exerting tension is 2 irr and its force is 2wrT; 
the volume of liquid raised is 7rr 2 h, and its weight icr 2 hw\ equating 

these, 2 7i7* r = irr 2 hw, 

2 T 
whence, h = (B) 

wr 



CAPILLARITY 



69 




This height would be the same as with the plates if r = b; if the 
diameter of the tube is equal to the width between the plates, 
r = J b, and the height of rise in the tubes is twice as great as 
between the plates. Both with tubes and plates the rise of the 
liquid is inversely proportional to the width of the 
column. 

(Shown by capillary tubes as in Fig. 21.) 
In the case of the liquid raised between the 
two plates, the fluid pressure at the level surface 
outside the plates, as at A, Fig. 20 (1), is equal 
to the atmospheric pressure upon it, and it is the 
same as this at all points in the liquid at the same 
level, as at C. Above C there is a column of Fig. 21.— Rise of 
liquid to B, and upon that the atmosphere. Liquids by Cap- 
The pressure in the liquid at B is less than at 
C to the extent that the surface tension at the top of the column 
has opposed the weight of the atmosphere; i.e., to the extent of 
the pressure due to the height BC of the liquid. (See Art. 52, 
Note.) Upon that part of the plates between which there is a 
liquid column, the pressure of the liquid outward against the 
plates is less than the pressure of the atmosphere on the outside 
forcing the plates together. Accordingly, if two clean glass 
plates are in contact except for a very thin layer of water which 
has a sharp curvature concave outward all along the edge of the 
stratum of water, the pressure of the liquid outward is less than 
that of the atmosphere, and the plates require a considerable 
force to separate them. The spread of a drop of water between 
the plates of itself pulls them together. If the water is thin 
enough to sustain a column 30 cm. in height, this would be ap- 
proximately 0.03 of an atmosphere in pressure, or the excess of 
pressure holding the plates together would be 30 grams per 
square centimeter. On plates 10 cm. square this would be a 
total pressure of 3 kg. 

On the other hand, if two such plates are forced together with 
a layer of mercury between them, the resistance becomes greater 
as the layer becomes thinner, forming an exceedingly elastic 



70 PROPERTIES OF MATTER; MECHANICS 

cushion. (See Tait, Properties of Matter, Chap. XII; also Glaze- 
brook, Laws and Properties of Matter; also article on " Capillar- 
ity " by Clerk Maxwell in Encyclopcedia Britannica.) 

Experiments Nos. 25 and 26, page 97 , showing capillary sustaining force 
in tubes and between plates. 

Example. — If the surface tension of water is 81 dynes per centimeter, 
how high will water rise by capillarity in a glass tube one-tenth of a milli- 
meter in diameter? To what depth would mercury be depressed in the 
same tube if the surface tension is 540 dynes per centimeter? 

Ans. Water, 2>2> Cm -J mercury, 11.43 cm - 

54. Pneumatics. — The science of gases. As gases have a 
tendency to indefinite expansion, so, upon increase of pressure ; 
their volume may be reduced. 

Expansion on removal of pressure may be shown by rubber 
balloon or other thin closed vessel under receiver of air pump. 

Experiment No. 27, page 97. — Expansive Force of a Gas. 

55. Atmospheric Pressure. — The downward pressure of the 
atmosphere may be shown by the pressure of a receiver upon 
the plate of an air pump. (Action of the pump to be explained 
later.) 

Upward pressure may be shown by card under an inverted 
beaker full of water. 

Experiment No. 28, page 97. — That the water is not retained in the ves- 
sel by any effect of the card acting as an ordinary stopper may be shown by 
using a beaker with the open end covered with mosquito netting. Placing 
the card in position as before, it is held up and the water does not es- 
cape; but while the vessel is thus inverted the card may be taken away 
and still the water does not run out if the under surface is kept horizontal. 
The card may be dispensed with by simply placing the hand over the netting 
when inverting the beaker. (The surface film helps somewhat in supporting 
the liquid.) As soon as the beaker is inclined slightly, the pressure is different 
at different parts of the lower surface and the water escapes. (See Weinhold, 
Physikalische Demonstrationen, p. 203.) 

Experiment No. 2Q, page 98. — Pressure in all directions is shown by the 
fact that the Magdeburg hemispheres hold alike in every position, — - hori- 
zontal, vertical, or any other. 



BAROMETERS 7 1 

To calculate pressure holding the hemispheres together, com- 
pute pressure upon area of a great circle, not of the surface of a 
hemisphere. 

The original experiments with the air pump were conducted 
by Otto von Guericke at Magdeburg (1650-1672). 

Prior to the time of Galileo, the rise of water in a common 
pump, and similar phenomena, were ascribed to Nature's horror 
of a vacuum, and as early as 1640 Galileo had made attempts 
to weigh air. In 1643 Torricelli, a pupil of Galileo, measured 
the extent of the horror vacui by means of the mercury column 
in a long tube, forming the ordinary barometer column, with 
what is known as a Torricellian vacuum above it. He thus 
showed that Nature's horror of a vacuum did not extend above 
about 76 cm. of mercury, and he was able to determine the 
weight of the atmosphere. At the earth's surface the pressure 
of the air is equal to the weight of a column of air, everywhere as 
dense as at the earth, five miles high. If a vacuum were formed, 
air would rush in to close it with a velocity equal to that of a 
body that has fallen from a height of five miles under gravity, 
or about 1300 feet per second. (See infra, Art. 61.) 

Torricelli's work was confirmed and extended by Pascal, with 
columns of various kinds of liquids, 1647-1653. Pascal showed 
(1648) that the height of the mercury column, or any liquid 
similarly supported, is due to air pressure. After the experi- 
ments of his brother-in-law, Perier, at Puy de Dome, Clermont (a 
mountain about 4300 feet high), in which experiments the barom- 
eter showed the (to Pascal) astonishing difference of over three 
inches at the foot and at the top of the mountain, Pascal made 
various further experiments at lesser heights in the tower of the 
church of St. Jaques, Paris, about 150 feet high. 

Investigations of air and air pressure were made by Robert 
Boyle, and by Mario tte, about 1660. 

56. Barometers. — Mercurial, aneroid; exhibit and describe. 
Standard barometer height is 76 cm. height of mercury column 
at temperature of o° C, at sea level in latitude of 45 °. Lowest 
barometer record for New York was 28.61 inches, January 3, 
I9I3- 



72 



PROPERTIES OF MATTER; MECHANICS 



(Correction of barometer; see Watson, Arts. 132 and 134.) 
Height of the atmosphere. 

57. Boyle's Law. — Temperature remaining constant, the vol- 
ume of any given mass of gas varies inversely as its pressure. 

z;oc-or v = k- 7 whence pv = k, where 
P P 

k is a constant depending on the 

units in which p and v are measured. 

In Fig. 22 (a), if the tube is of 
uniform bore the volume of any 
part of it may be represented by 
its length; if mercury is at the level 
A in both arms of the tube to begin, 
and AB is an inclosed volume V of 
air under atmospheric (barometer) 
pressure, say volume 10 cm. and pres- 
sure 76 cm., VP = 760. When mer- 
cury is poured in at E until it stands 
at D and C, then CB — v, p = 76 + 
height CD, and (») (76 + CD) = VP = 
760, and so on. 

In (b), suppose AB = V = 10, and 

P = 76, VP = 760; when B is raised 

( a ) ( & ) until volume of air = v, then p = 76 

Fig. 22. Boyle's Law. _ height of mercury in tube, and 

(v) (76 — height of mercury in tube) = VP = 760, etc. 




(Avoid haste in taking measurements, also in compressing and expanding 
the air on account of changing temperature. Distinguish between demon- 
stration and illustration of a law.) 

Examples. — 

1. An air-tight piston 1 inch long is at the middle of a closed cylinder 
11 inches long. The piston is pushed to within a half-inch of one of the 
ends. Compare the pressure on each side of it. Ans. 19 : 1. 

2. In Fig. 22 (b), when the mercury is at the same level within and 
without the tube, suppose the length of air column in AB to be 30 cm. and 



DEVIATIONS FROM BOYLE'S LAW 73 

pressure of the atmosphere 76 cm. When the tube is raised so that the 
mercury within is 10 cm. above that without, how much are the pressure 
and volume of the air in the tube altered? 

Ans. Pressure is ft and volume ft as great as at first. 

3. A bicycle pump with stroke of 12 inches is full of air at 15 pounds per 
square inch. Supposing the air is not heated by compression, how far 
must the piston move before air will be forced into the tire at 40 pounds 
per square inch above atmospheric pressure? (Franklin and Macnutt's 
Mechanics.) Ans. ■ 8.73 inches. 

4. An inverted test tube 30 cm. long and of uniform cross-section is just 
submerged vertically in water. If the barometer reads 76 cm., how high 
does the water rise in the tube? Ans. 0.824 cm. 

58. Deviations from Boyle's Law. — If Boyle's law were 
strictly true, then for a given mass of gas at a given temperature, 
no matter how the pressure ever varied, the volume would change 
so that the product PV would always be the same. It is found, 
however, that gases under great pressure approach a change 
from gaseous to liquid condition, especially if their temperature 
is low; and some gases are ready to change into liquids at a 
moderate pressure even at a temperature that is not low (steam, 
for example, liquefies under one atmosphere pressure at a tempera- 
ture of ioo° C). 

Now gases which conform to Boyle's law very closely at tem- 
peratures and pressures remote from the point of liquefaction 
are found to depart sensibly from the law when near liquefaction. 
An increase of pressure is not attended by a proportional diminu- 
tion of volume, so as to make PV constant, but nearly all gases 
for a limited range of high pressures are slightly more com- 
pressible than to agree with Boyle's law; i.e., if the pressure is 
increased a certain fractional part, the volume is diminished 
by a greater fractional part, so that PV becomes smaller as the 
pressure increases. Hydrogen is an exception. It is all the 
time less compressible, so that PV increases. With other gases 
PV decreases to a minimum, and then, as the gas approaches 
liquef action, PV increases. 

On a diagram (Fig. 23) showing pressures by horizontal dis- 
tances, and values of PV by vertical distances, PV decreases, 



74 



PROPERTIES OF MATTER; MECHANICS 



35 










1 


&£ 














30 




\ 






vo? 


o^ 




** 


^ 




° 




•V- 




C 








;\f v 


o^ 












25 

•> 


\ 




s, 


\ 












jf! 


fcx 










f\ 




V 


s 






d$ 


W 












u-20 
O 




\ 










c 










X" 








\ 
















« 


f 








in 
















& 


Pi 






















oO 


*> 
















2,0 










6 


-y£> 














































5 

























































































with an increase of P for a while, the curve sloping downward; 
and then as P is further increased, PV also increases, giving a 

curve sloping up. If PV 
were constant, the curve 
'would be a horizontal line. 
The significance of this will 
be brought out more fully 
under the subject Heat. 

It is seen, however, that 
Boyle's law is very nearly 
true for gases in a high state 
of attenuation. The particles 
of a gas may then be thought 
to be in some sense analogous 
to those of a substance dis- 
solved in water, if the solu- 
tion is very dilute. (See article " Osmosis.") 

59. Elasticity of a Gas at Constant Temperature. — If the 
gas conforms to Boyle's law, suppose we have a volume V at 
pressure P. Then the volume will be diminished in just the 
same proportion that the pressure is increased. If to P is added 

p 
a small pressure p, this is ^ part of the original pressure, and 

the volume will be diminished ~ part of the original volume, 

P 
or the decrease in volume is ^ V. Now the strain is the ratio of 

P 
the change of volume to the original volume, or ^ V -5- V, or the 

P 



50 100 150 200 250 300 
PRESSURE IN METERS OF MERCURY. 

Fig. 23. Departure of Gases from Boyle's 

Law at High Pressures. 



strain equals 



P' 



The stress is p, and 
elasticity = 



stress _ £ _ p 



strain 



P 
P 



That is to say, for a gas at constant temperature, the elasticity 
is equal to the pressure, a result that we shall recur to in the 
study of sound. 



VELOCITY OF EFFLUX 



75 



Note. — This may be more simply shown by the calculus. If PV = const., 
P and V being both variable, then by differentiating, P dV -\- V dP = o; whence 



dP P 

dv = ~v> or 



stress 
strain 



VdP 
dV 



V^ = P. 
dV 

= P. 



dV 
Now dP = stress and — = strain and E = 



60. Air Pumps. — Exhibit and operate: gauges, barometer 
column, siphon gauge, McLeod gauge (see Barker, p. 199); the 
Fleuss pump sold under the name "Geryk" vacuum pump, 
described in Watson, p. 155; mercury pumps, — Sprengel, Geiss- 
ler (see S. P. Thompson, Development of Mercurial Air Pump). 

61. Velocity of Efflux. — If a liquid is at rest in a vessel, 
as in Fig. 24, the pressure outward, due to the liquid, at a point 
B is proportional to AB, the depth 
of B below the free surface of the 
liquid. The total pressure is that 
due to the weight of the liquid and 
of the atmosphere above it. If an 
orifice is opened at B, there will be 
a back pressure of the atmosphere 
at B. The excess of pressure, then, 
to force the liquid out at B, is that 
due to the weight of the liquid from 
B to A. This excess of pressure 
with the liquid at rest represents potential energy at B equal in 
amount to the work of raising the liquid from B to A. If the 
liquid at B is not held so as to exert pressure against the vessel, 
but is free to escape, its potential energy is at once changed into 
kinetic energy, and the velocity of any mass m escaping is given 
by the equation 



Fig. 24. Efflux of a Liquid. 



mi 



= J mv 2 , whence v 2 = 2 gh. 



This is independent of the density of the fluid. If, instead of a 
simple orifice at B, there is a pipe for outflow with a smaller 
orifice at the extremity C, calling v the velocity of efflux at C and 
v' the velocity of flow within the pipe BC, v' will be smaller than 
v and there will be a pressure p' upon the sides of the pipe to 



76 PROPERTIES OF MATTER; MECHANICS 

correspond to a head h! smaller than h, so that mgh' -f- \ mv' 2 = 
mgh, and v' 2 = 2 g(h — h'). 

62. Aspirating Action of Flow. — When a fluid is flowing 
through a pipe of uniform bore, if we neglect the additional force 
required merely to overcome the friction of the walls of the tube, 
the static pressure due to a given head will be the same at all 
places where the velocity is the same, as at A and B, Fig. 25(a). 
But if at a point, as C, there is a narrowing of the pipe, the veloc- 
ity in the throat at C will be increased, and the outward pressure 
decreased, since the energy of the fluid itself is not altered. If 
C is connected with the air or with another vessel, there will be 
a suction into the pipe AB at C. 

If BB, Fig. 25 (b), is a perforated disk attached to the pipe A, 
and DD is a light disk close beneath it, by blowing through A the 

air escapes through the small 
> ^c^ > ' space C, with a correspond- 

ingly increased velocity and, 
therefore, diminished pressure 
against the plate DD, and the 
latter rises and is held up 
against BB, and harder the 

I R harder it is blown against. 

/ — - (h\ T . . , . .,..„., 



(a) 



(b) 



p £ ; It might seem that if the air 

Fig. 25 . Aspirating Action of Flow. between BB and DD has less 

pressure than the external air 
it would not escape, but it is the pressure transverse to the 
direction of motion whose diminution permits the rise of DD. 

The added effect of the velocity gives the escaping air at the 
rim a total of energy due to the pressure and velocity greater 
than the energy equivalent to the pressure of the external air. 
This might be true even if the pressure within the space C to 
hold the plates apart is very small. Of course the velocity of 
the escaping air would have to be very great. (See Hastings 
and Beach, Art. 100; also article on "Bernoulli's Principle," by 
W. S. Franklin, in School Science and Mathematics for January, 
1911.) 



SIPHONS: SAFETY, INTERMITTING 



77 



63. Siphons : Safety, Intermitting. — To explain the action 
of the siphon, consider the forces acting to drive the liquid past 
the highest point B in Fig. 26. 

The force to drive the liquid from right to left is the atmos- 
pheric pressure at A minus 
the pressure of the liquid 
column of vertical height 
from B to A; the force to 
drive from left to right is 
the atmospheric pressure at 
E minus the pressure of the 
liquid column of vertical * 
height from B to E. Pres- 
sure to left exceeds that to 




Fig. 26. 



G 

The Siphon. 



right by pressure of liquid column of vertical height equal to the 
difference between levels of A and E. 

The intermitting siphon is sometimes arranged as a Tantalus 
vase (Fig. 27 (a)), the siphon being concealed within the body of 
the figure of a man of such height that the water 
rises nearly to his lips and then recedes. 

Tantalus, having offended Jupiter by intem- 
perate language, was consigned to Tartaros, and 
there punished as described by Homer, who 
makes Odysseus say: "And I saw Tantalus 
suffering grievous torments, standing in a lake, 
and the water dashed against his chin, but he 
resembled one thirsty, and could not take any to 
drink, for as often as the old man stooped, eager 
to drink, so often the water disappeared, being 
He only forgot his thirst in hearing the music 
of Orpheus. Origin of the word " tantalize." 

The explanation of intermittent springs by a large cavity within 
a hill or mountain, from which a siphon-shaped channel leads, 
is discredited by geologists and physiographers as highly im- 
probable, though it is possible that a siphon might be formed and 
its action occur intermittently by fissures and strata, somewhat 




Fig. 27 (a). Tan- 
talus' Vase. 

absorbed," etc. 



78 



PROPERTIES OF MATTER; MECHANICS 



as roughly indicated in Fig. 27 (b), where BCDE is fed by several 
veins as A A and discharged through the longer leg EF, the water 




Fig. 27 (b). Intermittent Spring. 



issuing from the soil finally at S. If efflux from 5 is more rapid 
than influx at B, the flow at 5 ceases when CDEF is emptied and 
resumes when it is filled. (Martonne, Traite 
de geographie physique.) 

Since the velocity of efflux from a siphon is 
determined by the height from the orifice of 
efflux to the surface of the liquid, it is inde- 
pendent of the nature of the liquid. 

64. Mariotte's Flask. — This is a flask 
(Fig. 28) with side tubulures a, b, c, etc., for 
efflux of liquid, and a tube fitted air-tight, but 
which can be slid up and down through the 
stopper, thus fixing the height of the lower 
extremity d at pleasure. If d is higher 
than b the liquid escapes at b and the pressure in the space 
s above the liquid is slightly diminished, air entering at d. At 
d the pressure is just that of the atmosphere; from d upwards 
through the liquid the pressure diminishes and the air in bubbles 
rises, maintaining an air pressure in s which, added to the pres- 
sure of the liquid column sd, equals the pressure of the atmos- 
phere. From d downwards the pressure increases and at b its 




Fig. 28. Mariotte's 
Bottle. 



KINETIC THEORY OF THE STRUCTURE OF MATTER 



79 



excess over that of the atmosphere is equal to that due to the 
height from b to d. This being kept constant, the velocity of 
efflux is constant, no matter what the depth of the liquid in the 
flask, so long as its surface is higher than d. The velocity can be 
regulated by the position of d. If d is below the level of the tubu- 
lure that is open, the liquid will not escape from that opening, and 
it will stand in the tube cd at the level of 
that opening. 

The intermittent fountain (Fig. 29) 
illustrates the failure of a liquid to flow 
out of a vessel if the pressure of the air 
and liquid within the vessel is less than 
that of the atmosphere. 

A large vessel C is closed air-tight at 
top and bottom but has one or more 
small orifices D through which water 
can flow out. A tube A , open at both 
ends, extends from the top of C nearly to 
the level of the basin B. Through a 
small orifice in the bottom of the basin 
liquid can escape, but not so rapidly as 
from the orifices D. As the water flows 
out of C air continually enters below, but the basin gradually 
fills up until the lower end of the tube A is closed. The action 
of the fountain then ceases until the water escaping from B 
opens the tube at the lower end, and the operation repeats itself. 

65. Pumps. — Illustrate by model and diagram. An appli- 
cation of Boyle's law. Enlargement of air space under piston 
decreases the air pressure in it, and water rises under the excess 
of atmospheric pressure outside of the pump. Suction not a 
force but only a permission for excess of pressure to act. 

66. Kinetic Theory of the Structure of Matter. — (Prelimi- 
nary to Heat.) (See Watson's Physics, Arts. 140, 141; then 
Arts. 162, 163 and 164.) 

This theory has nothing to do with the ultimate nature of 
matter, but sets out with the idea of atomic structure, and 




Fig. 29. Intermittent 
Fountain. 



80 PROPERTIES OF MATTER; MECHANICS 

proceeds with the combinations of atoms in the form of mole- 
cules, which are separate from one another and are perfectly 
elastic. The molecule is the elementary form, though the mole- 
cule may be a combination of several atoms, and the atom an 
aggregation of many corpuscles (or electrons). The theory ap- 
plies to liquids and solids as well as to gases, but it is most 
readily exploited in connection with the gaseous form of matter, 
the essential ideas being embraced in the following seven propo- 
sitions (see Wormell's Thermodynamics, pp. 154 to 160). 

(1) The molecules of the same gas must be alike, but those 
of different gases must differ in properties or in structure. They 
must be separated by intervals which are very great compared 
with the size of the molecules. 

(2) The molecules of a gas move in straight lines. 

(3) When the molecules come into contact, they impinge so 
that their directions of motion change. 

(4) All the molecules of the same gas have the same mass, 
and when they impinge they always rebound. 

(5) In the same gas or mixture of gases the mean energy for 
each particle is the same. 

(6) The pressure of a gas per unit of area is proportional to 
the number of molecules in a unit of volume and to the average 
energy with which each strikes this area. 

(7) The pressure per unit area is proportional to the density 
of the gas and to the average square of the velocity. 

The first five of these propositions being postulated, or accepted 
as not inconsistent, the last two call for demonstration. 

For proposition 6, concerning the pressure exerted by a gas: 
Conceive of a cubical vessel, with one centimeter length of edge, 
filled with a gas of which each molecule has a mass m. Suppose 
the directions of the edges to be W.-E., N.-S., up-down. If the 
number of molecules is very great, the effect of their movement 
at any instant in all directions will be the same as if one-third 
of them were moving parallel to the W.-E. edge, one-third 
parallel to the N.-S. edge, and one-third parallel to the up-down 
edge. Also we may assume an average velocity for a particle 



MEAN VELOCITY OF THE MOLECULES OF A GAS 81 

in each of these directions, and call it V. When a molecule of 
mass m impinges upon a side of the vessel with a velocity V and 
rebounds with an equal velocity in the opposite direction, its 
change of momentum is 2 mV. This will occur against the same 
face of the cube for one molecule as often as the molecule goes 
across the cube and back, or a distance of 2 cm. The time 
to travel 2 cm. is 2/V. Therefore, for one molecule a change of 
momentum of 2 mV is made in 2/V seconds. Since the force 
thus exerted is expressed by the relation 

force X time = change of momentum, 
the force here is the rate at which momentum is changed; i.e., it 
is for each molecule 2 mV divided by 2/V or mV . 

If N is the total number of molecules in this cubic centimeter 
of gas, then J N may be considered the number moving parallel 
to one edge at any time, and therefore the number whose re- 
bound causes the pressure on one face of the cube (or vessel con- 
taining the gas). The total pressure, therefore, on one face of 

the cube, or the pressure per square centimeter in any direction, 

— 2 
is p = J NmV . The total kinetic energy of N molecules is 

J NmV . p, therefore, is proportional to the kinetic energy, 

being equal numerically for unit cube to two-thirds of it. Q.E.D. 

(Cf.Exs. (a) and (d), Art. 21.) 

67. Mean Velocity of the Molecules of a Gas. — Let p = 

density of a gas ; this is the mass per unit volume, and if m is 

the mass of one molecule and N the number of molecules in unit 

volume, p = Nm. From the preceding article p = \ NmV 2 , and 

— 2 
if for Nm we put p, then p = \ pV . This proves proposition 

4) 1 — 2 
(7). Then - = - V . If M = the entire mass of any quantity 

P 3 

M . I ~Ji 

of gas, and v its volume, then p = — , and since p = - pV sub- 

v 3 

stituting in this the value of p we get 

pv = iMV 2 = i-hMV\ 
That is, if M is the mass of a given volume, the product of the 
pressure by the volume is two-thirds of the energy of translation 
of the molecules of that gas. 



82 



PROPERTIES OF MATTER; MECHANICS 



With a gas that conforms to Boyle's law, for any given tem- 
perature pv = const., and since the density is the ratio of mass to 

M 
volume, if the total mass of the gas is M its density p = — , or 

v 

][/[ j) <n <h<D 

v = —, and pv = -M. Therefore, for a given mass M , — = ^rz. 
p p p M 

i) I — 2 I — 2 

= const. But we have just seen that — = - V , therefore,- V 

P 3 3 

— 2 

= const, or V = const. Hence, if Boyle's law holds, the mean 

velocity of the molecules is constant. From the equation - = - F 2 , 

P 3 



we have V 



= v/ 



IP 



Therefore, if we know the pressure and 



density of a gas, we can compute the mean velocity of its mole- 
cules. The formula shows that the mean velocity is inversely 
proportional to the square root of the density. Under a pressure 
of one atmosphere, 1,013,250 dynes per sq. cm. at the tempera- 
ture of o° C.,* we have: 



Hydrogen 

Nitrogen 

Air 

Oxygen 

Carbon dioxide 

Chlorine 



. 0000896 

.001257 

.001293 

.001430 

.001974 

•003133 



V, cm. /sec. 



185,000 
49,400 
48,700 
46,500 
39,600 

Students 
Compute 



p, compared 
toH. 



I 
I4-03 

14-43 
15.96 
22.03 

34-97 



68. Diffusion. — (a) Gases: Since it is characteristic of a 
gas to fill any space that is open to it, the kinetic theory readily 
prepares us for the fact that two different gases in communicating 
vessels diffuse into each other; and this will take place even 
through a septum between them if the partition is porous, like 
a coarse membrane or unglazed earthenware. It is found that 

* This is the value of one atmosphere by taking the exact figures for density 
of mercury = 13.596, the standard barometer height = 76 cm., and the accelera- 
tion of gravity in latitude 45° = 980.6 cm./sec. 2 . For any other latitude X at 
sea level, g = 980. 506 — 2.5028 cos 2 A (See Hastings and Beach, General Physics, 
Art. 30). 



OSMOSIS 83 

the rate of passage through such a partition, which is really 
passage through very small orifices or tubes, is inversely propor- 
tional to the square root of the density. If r is the actual 
velocity with which the gas moves through the partition 

r = \—* (For demonstration, see Watson, Art. 138.) If two 

bottles, one containing, say, hydrogen, and the other carbon 
dioxide, both at atmospheric pressure, are thus placed in com- 
munication through a porous septum, each will at once begin to 
diffuse into the other at a rate inversely as the square roots of 
their densities; that is, the hydrogen will enter the C0 2 at a much 
greater rate than the C0 2 enters the hydrogen, the pressure in 
the C0 2 bottle increasing and that in the hydrogen decreasing. 
Eventually this disparity in the rate will change with change of 
pressure, and diffusion will cease when the gases have become 
intimately mixed. 

Experiment No. 30, page 98. — Diffusion of Illuminating Gas through 
Porous Cup. 

(b) Liquids: This phenomenon, in connection with the pres- 
sure produced by the more rapid diffusion in one direction than 
in the other, has opened up some interesting facts with liquids. 
Here diffusion is more to be wondered at than with gases, since 
liquids have no tendency to expansion, and under gravity they 
rest on their base and exert a pressure downward. And yet, if, 
of two liquids that are miscible, the lighter one rests directly 
upon the heavier one in the same vessel, not only does the upper 
one gradually sink into the lower, but the lower, heavier one 
rises, contrary to gravity, into and through the upper one. 

Experiment No. 31, page 99. — Diffusion of Liquids. 

69. Osmosis. — This process of diffusion will take place even 
if one liquid, say, a dilute solution of sugar, is inclosed in a porous 
sack and dipped into the other, say, water. In such case the 
pressure in the sack is materially increased by the greater rate 
of diffusion of water into the (denser) solution. This pressure, 
called osmotic pressure, varies with the density of the solution 



8 4 



PROPERTIES OF MATTER; MECHANICS 



and with the nature of the substance dissolved. The explanation 
of osmotic pressure by the kinetic theory is that "the semi- 
permeable membrane is struck on both sides by water molecules, 
but since there are fewer water molecules per unit volume, some 
of the space being occupied by sugar molecules which cannot 
traverse the membrane, more water molecules will, in a given 
time, strike the outside than the inside of the membrane, and 
hence, as the water molecules can pass through the membrane, 
more water molecules will enter than leave." (Watson, Art. 
164.) 

Now, when the substance is dissolved, it may be considered as 
distributed throughout or occupying the entire volume, and if 
we take a definite mass, say one gram, of sugar and dissolve in 
various quantities of water, thus giving to this gram various 
volumes, we find its osmotic pressure varying inversely as the 
volume, or pv = const., the substance when in solution conform- 
ing to Boyle's law for gases, provided the solution is dilute, as 
illustrated in the following table: 



Percentage of 
sugar in solu- 
tion. 


Osmotic pressure 
P, in cms. of Hg. 


Vol. V, of solution 

containing one gm. 

of sugar. 


PV. 


I 
2 

4 
6 


53-5 
101 .6 
208. 2 
307-5 


c.c. 
99.6 
49.6 
24.61 
16.34 


5239 
5039 
5124 
5025 



A peculiar consequence of the incessant movement of the 
molecules of a liquid or a gas is seen in the so-called Brownian 
movement. A body very large relatively to the molecules, when 
placed among them, may be at rest under the promiscuous 
bombardment which it receives on all sides, and any but very 
minute particles of matter are thus relatively large. But when 
they are so small as to be comparable with the molecules they 
are no longer in equilibrium, and are found to be incessantly 
in motion, irregularly driven hither and yon, so that the mole- 
cules themselves are unquestionably constantly shifting their 
position. (See Soddy, Matter and Energy, pp. 78, 91, and 103.) 



EXPERIMENTS TO ILLUSTRATE CHAPTER I. 



Experiment No. i, Art. ij. Vortex Motion. 

A box of ordinary cardboard, Fig. 30, from six to ten inches on a side 
and six inches in depth, will serve. Laying the box on its side, with a cir- 
cular hole about three inches in ,.' ' ^ 

f \ { • % 
diameter in the front (i.e,, bot- ,:>r\7^r 

torn of the box), the circular 
steady vortices are formed. By 
having a card as a flap that can 
be turned over the front, with 
an elliptical hole with axes 
about one and a half inches and 
three inches, the vibrating vor- 
tices are produced. The drum- Fi - 3 °' Vortex Rings, 
head at the back of the box may be a light frame fitting the box and having 
a piece of chamois skin stretched over it. A slight tap on the chamois in 
the line of the orifice is sufficient to expel a ring. 






Fig. 31. Time-ele- 
ment in Inertia. 



Experiment No. 2, Art. 17. Nos. 2 to 5, incl., Illustrate 
Inertia. 

To a body weighing four or five pounds attach a 
portion of string, both above and below, that is just 
strong enough to carry a little more than the given 
weight. If the body is lying on the table, with 
deliberation it may be lifted by means of the upper 
string, but if the attempt is made to lift it suddenly 
the string breaks. If the weight is suspended, as in 
Fig. 31, a steady pull on the lower cord is trans- 
mitted to the upper one, which has to sustain the 
weight and the added pull. If the latter is gradually 
increased, the upper string breaks; if, however, the 
lower string is sharply jerked, it is broken, while the 
upper one is not affected. Before the force that is 
suddenly applied to one cord has time to overcome 
the inertia of the large mass (or to accelerate it) 
sufficiently to increase the tension in the other cord, it 
is itself broken. 
85 



86 PROPERTIES OF MATTER; MECHANICS 

Experiment No. j, Art. 17. 

Place a coin on a card; if it is not moved too rapidly the coin can be 
carried around on the card without slipping. Put the card and coin over 
the mouth of a narrow beaker or wide-necked bottle; flip the card sharply 
horizontally and it flies out without moving the coin, which drops into the 
vessel. The experiment admits of innumerable variations. 

Cut a strip of ordinary writing paper about four centimeters wide and 
twenty-five centimeters long. Let about one-third of its length lie on the 
table, while the unsupported end is held by the thumb and finger of the left 
hand. A disk or coin, or even a pile of a dozen of them, laid on the part of 
the strip that is over the table moves readily about with the paper as this 
is pushed or pulled around, but if the strip is struck downward sharply be- 
tween the left hand and the table, it is jerked out, while the disk remains 
undisturbed. The less surface of contact there is between the disk and the 
strip the better. With a nickel five-cent piece standing on edge, with its 
faces parallel to the length of the strip, the effect is more striking. 

Experiment No. 4, Art. 17. 

On the shaft of an electric motor making 1000 to 1500 revolutions per 
minute, mount a hub of four to six inches in diameter. A light endless 
chain, of such length that when placed on the hub it hangs several inches 
below it, is so suspended and the motor started. When the disk has brought 
the flexible chain to its own speed, the latter will be found to have acquired 
considerable rigidity, and if it be carefully slid from the hub, and allowed to 
drop a few inches to the table, it will rebound and skip and roll some dis- 
tance, like a hoop, before it collapses. 

While the chain is in motion on the hub, it may be made to take various 
positions which persist apparently in opposition to gravity. By pressing 
it with a light roller that does not greatly impede its motion, it may be made 
to take an inclined or nearly horizontal position, which it maintains with 
the free end of the loop unsupported. (See Goodeve's Principles of Me- 
chanics, Art. 36.) 

Experiment No. 5, Art. 18. FoucanWs Experiment. 

In a place as free as possible from drafts and jars, suspend a heavy 
ball (ten pounds or more in weight) by a fine wire twenty feet or more in 
length. The upper support should be rigid, and under the bob should be 
fixed a. bristle or fine wire stylus. A board several feet in length and hinged 
at one end can be adjusted at such a height that when it is level the stylus 
will just touch a smoked-glass plate on the board, and when the free end 
is lowered, the stylus will pass clear of the glass. 

The bob is drawn back about a foot or eighteen inches from the vertical 
. and secured in that position until all sidewise motion has ceased. It must 



EXPERIMENTS 



87 



also be carefully adjusted so that when released it will not take on any 
rotary motion. A good plan for releasing it without shock is to draw it 
back by means of a cord attached to a ring of spring wire somewhat larger 
in diameter than the bob. When the cord is burned off by a match, the 
wire loop springs open and drops off. After the pendulum has thus been 
set swinging, at an observed instant the board is raised to the horizontal 
and a mark is made by the stylus as it passes over the plate. The board is 
at once lowered and the pendulum is left 
swinging. At the end of a half-hour another 
record may be thus taken, and again in 
another half-hour. By this time the pen- 
dulum will probably be swinging in a narrow 
ellipse, so that the three lines may not inter- 
sect in a common point; but the angular 
deviation of the plane of oscillation in each 
half -hour can be readily measured when the 
smoked glass is removed from its table, and 
the records may be projected upon the 
screen. 

More elaborate methods both of sus- 
pension and of recording may be used to 
advantage. 

The elliptical path into which the pen- 
dulum is almost certain to fall is probably 
due to the fact that no wire for suspension 
can be obtained that is everywhere round; 
the cross-section will have unequal diame- 
ters, and the wire will be stiffer in one direction than in a direction at right 
angles to that. 

The fewer the oscillations made by the pendulum the less will be the 
disturbance in this respect; hence the advantage of a long wire, and corre- 
spondingly long period. Also, the heavier the bob the smaller the dis- 
turbance from air currents or other slight causes. 




Fig. 32. Foucault Pendulum. 



Experiment No. 6, Art. 20. Independent Action of Simultaneous Forces. 

If two balls at the same height above the floor are so arranged that 
when one is violently projected horizontally the other drops vertically at 
the same instant, they reach the floor at the same time. 

Numerous contrivances have been devised, of which Fig. 33 shows one 
that is simple and convenient for frequent use. On a base board AB is 
pivoted by a screw another board CD, about 40 cm. long and 5 cm. broad. 
The edge of CD is about two centimeters from the edge of AB, and under 



PROPERTIES OF MATTER; MECHANICS 



one end of CD is fastened a piece of sheet tin about two by four centimeters. 
This board can be placed upon any table, and with balls as in the figure, a 





Fig. 33. One Ball is projected horizontally while another is dropped vertically. 

blow against CD at C projects one ball and drops the other at the same 
instant. Both strike the floor at the same time. 

Experiment No. 7, Art. 23. Concurrent Forces. 
Since when three forces are in equilibrium either one is equal and opposite 
to the resultant of the other two, by an arrangement of spring balances as in 




Fig. 34. Equilibrium under Three Forces 



Fig. 34 {a) the three forces can be adjusted to any variety of magnitude and 
position (but passing through a common point), and one will be represented 
by the diagonal of the parallelogram constructed upon the other two, or it 
will form the third side of a triangle in sequence with the other two. 



EXPERIMENTS 



89 



An arrangement like Fig. 34 (b) serves the same purpose. In fact, in 
either case it is not necessary to know the actual magnitude of more than 
one of the three forces, except to prove the correctness of the experiment. 

Experiment No. 8, Arts. 17 and 25. Centrifugal Force. 
If a looped chain be suspended by a thread from the spindle of a whirling 
table, Fig. 35, and be set rotating about the vertical, it will widen out and 




Fig. 35. Whirling Chain, etc. 

at first produce a pear-shaped figure, but as the speed increases it passes 
through the forms 1, 2, 3, and finally places itself in the position 4, in which 
every link is as far from the axis of rotation as possible. The large gain of 
energy by the chain is now partly kinetic, corresponding to the rotation, and 
partly potential, corresponding to the higher position which the chain now 
occupies as a whole, compared to the position 1. If instead of a chain a solid 
ring be suspended as AB, on rotating it the ring takes the position D; always 
the position which most nearly permits every particle to move on in a 
straight line. 

If a round flask be suspended instead of the chain or ring, and liquids 
of different densities, say mercury and water, be placed in it, on rotating, the 
liquid of greater mass displaces the other, showing that the centrifugal force 
is greater with the greater mass for any given speed and radius. 

Experiment No. g, Art. 27. Determination of g. 
From a helical spring which vibrates rapidly without any added weight, 
suspend as great a weight as the spring will permit without being per- 
manently distorted. Measure the extension produced by the weight, and 
time its oscillations, taking the mean of several observations. If elongation 



is e and period T, 



g = 



4 7r 2 e 



go 



PROPERTIES OF MATTER; MECHANICS 



Experiment No. 10, Art. 28. Bodies 
Falling in a Vacuum. 

The water hammer, Fig. 36 (a), is 
a tube and bulb containing water 
and vapor at very low pressure; 
when suddenly inverted the water 
column falls like a solid, striking the 
bottom of the tube with a blow like 
that of a hammer, and the drops 
through the throat from the bulb fall 
into the water with a sharp metallic 
click. 

(b) is the common guinea and 
feather tube. It usually contains a 
few leaden shot and irregularly 
shaped pieces of paper. When the 
stopcock is open there is full air pres- 
sure in the tube, and in a vertical 
position the lead balls drop quickly, 
while the paper saunters after them 
lazily. When the air has been ex- 
hausted from the tube, and the latter 
is turned into a vertical position 
F^ 3 5 < promptly, the paper and the lead 

Water Hammer. Guinea and Feather dart to the bottom of the tube 
Tube. together. 




(b) 



Experiment No. 11, Art. 34. Mechanical Paradox. 
Both the double cone and the cylinder, Fig. 37, illustrate a body rolling 
up hill under gravity, and also the tendency of potential energy to reduce 
to a minimum. 





Fig. 37. Bodies Rolling up Hill. 



Experiment No. 12. Art. 35. Galileo's Method of Determining g. 
A piano wire AB (Fig. 38), say, ten meters long, is stretched across 
the room, with a descent AC of about one meter. A light grooved pulley 



EXPERIMENTS 



91 



carries a weight of 100 g. to 200 g., and is released from A at a signal when 
a stop watch is started. When the pulley reaches B the watch is stopped and 




the time of descent noted, 
is traversed in time / is 



Fig. 38. 

With uniform acceleration a, the distance / that 
/ 



whence 

Theoretically, on the plane BAC, 



at\ 
2/ 



(A) 



(B) 



r lV 



Substituting the value of a from Eq. (A) in Eq. (B), we have g = t(-) 

Instead of the wire and pulley, Galileo used a grooved board down which 
balls were rolled. This avoids the sag in the wire. 

Experiment No. 13, Art. 35. Forces and Displacements. 

Besides the ordinary illustrations of levers, inclined plane, pulley, etc., 
the following well illustrates the principle of this article. 

Fig. 39 shows a model that may be turned out of wood, or constructed 
of cardboard or heavy manila paper. The diameters, and consequently the 
circumferences, of the end and the middle 
portions of the roller have a definite 
simple ratio, say 4:5. 

Two threads are attached to the end 
portions, wound round a few times, and 
then fastened to the hooks in the frame 
above. Two other threads are attached 
to the thicker part of the roller, given a 
few turns round it in the reverse direction 
to the first ones, and their ends connected 
by a stick whose weight is negligible. The 
weight necessary to put upon this cross- 
bar to prevent the roller from descend- 
ing is determined by these considerations: 
Suppose the roller makes one com- 
plete turn in descending; it unwinds the Fig. 39- Rolling Pin Model. 




9 2 



PROPERTIES OF MATTER; MECHANICS 



outer strings and thus lowers the whole system a distance equal to the cir- 
cumference of the smaller cylinders, but it winds up the cords on the larger 
cylinder and so raises the bar and weight a distance equal to the larger 
circumference. Suppose the smaller circumference to be, say, 12 cm. and 
the larger 15 cm.; then a descent of the roller and weight a distance of 
12 cm. is attended by a rise of the weight a distance of 15 cm., so that the 
actual rise of the weight is 3 cm., or one-fourth as far as the roller descends. 
For equilibrium of roller and weight, the work of the cylinder in descending 
must equal that of raising the weight, or weight of roller X distance it 
descends = wt. of W X height it ascends; i.e., with the above dimensions, 
W = A 
R 1 



or W = 4 R. A convenient size is about 15 cm. in length for the 



roller altogether, and the diameters of the two parts 10 cm. and 12 cm. 

Experiment No. 14, Art. 45. The 
Principle of Archimedes. 
The original Archimedean 
demonstration is the one best 
suited for lecture purposes. In 
the figure (Fig. 40), the cylinder 
A" underneath just fills the cylin- 
drical vessel A' from which it is 
suspended. The cup and cylinder 
as suspended from one arm of a 
balance are exactly counterpoised 
by weights in the pan at the end 
of the other arm, before the vessel 
of liquid is used. When the 
cylinder is immersed in any liquid 
as in the figure, it no longer 
matches the weight in the other 
pan, but the balance is restored 
when the cup A' is exactly filled 
with the same kind of liquid as 
that in which the cylinder is 
immersed. 




Fig. 40. Cup and Cylinder Apparatus. 



Experiment No. 15, Art. 45. The Cartesian Diver. 
The figure of glass or porcelain, Fig. 41, is hollow, the cavity being open 
at the bottom, so that, when partly filled with water, air is inclosed in the 
upper space. The figure may be regarded as consisting of glass and the in- 
closed air. When it is submerged it displaces (or occupies the place of) a 
definite volume of water. The weight of this volume of water is then the 



EXPERIMENTS 



93 



measure of the lifting or buoyant effort upon the figure. If this is 
greater than the weight of the figure the latter rises, and a small portion 
of it will project above the surface of the water in the 
vessel. If now the air in the upper part of the vessel 
is compressed, the pressure upon the water in the vessel 
forces more water into the figure. The figure now dis- 
places (or occupies the place of) less water than before, 
and is accordingly buoyed up with less force. The 
figure itself is neither heavier nor lighter than before, 
but, because of the reduction in volume of the air in it, 
less water is displaced, and a smaller upward force acts 
upon it. If the force is less than the weight of the 
figure, the latter sinks by gravity. When the pressure 
at the top of the vessel is removed, the pressure of the 
air within the figure forces water out of it (displaces 
water), the buoyancy is increased, and the figure rises. 

(Instead of a wide-topped jar with a rubber sheet, 
a bottle with a tube through a rubber stopper may be 
used. An ordinary atomizer bulb on the tube makes it 
easy to apply or remove pressure.) 

The accompanying figure of a longitudinal section of a Holland sub- 
marine boat shows that the action of this is like that of the Cartesian diver. 
Compressed air is stored at high pressure in strong receivers. Low in the 
hull of the vessel is a series of chambers that can be opened to the water 




Fig. 41. The Car- 
tesian Diver. 




Fig. 42. Longitudinal Section through Holland Submarine Boat. (Early Form.) 
By courtesy of The Scientific American. 



outside. When they are full of water the vessel is heavier than the water 
it displaces and it sinks. By admitting air under pressure into one or more 
of these water tanks, water is driven out (displaced), and the buoyancy in- 
creases so as to float the vessel. 

In the more modern type of submersible boat the same principles are 
applied, but with the admission of water into the compartments the total 
water displaced nearly but not quite equals in weight the weight of the 
boat, and so the vessel remains afloat with a very small portion exposed. 



94 PROPERTIES OF MATTER; MECHANICS 

The vessel is driven completely beneath the water by having rudders so 
placed as to direct the boat downward when the propeller is in motion. 

Experiment No. 16, Art. 46. Cork Remains Submerged under Mercury. 

Select a strong glass tumbler with a bottom that is flat or slightly concave 
on its upper surface, and a cork stopper, about two centimeters in diameter 
and two or three centimeters in height, which is quite smooth and flat on 
its larger end. By means of the fingers, or a piece of wood or iron, hold this 
smooth face firmly against the bottom of the tumbler and pour mercury 
into the vessel until the cork is completely covered. The mercury will not 
readily pass under the cork, there is therefore no upward pressure against 
the cork, and it remains submerged when its support is removed. Though 
hidden from view, if the glass is raised it is plainly seen from beneath. 
With the least twitch to the cork, admitting mercury under it, it leaps to the 
suiface. 

Experiment No. 17, Art. 46. One Tube Falls Upward into Another. 
Select two test tubes of such size that one may be inserted in the other 
with very little play but without much friction. Holding the larger one 
vertical, fill it with water and push the smaller one, closed end down, into 
the larger, an inch or two. Then, holding both in place, invert the two and 
release the lower (smaller) one. Instead of falling out, it rises into the 
upper one, displacing the water above it, and continuing with an accelerated 
motion as far as the length of the tubes will permit. 

J Experiment No. 18, Art. 31. 

Determine the density of several liquids by Hare's 
apparatus, in each case taking the height of liquid 
/ columns at several different levels, and compare re- 
/ suits with readings of hydrometer. 

Experiment No. 19, Arts. 50 and 51. Two Vessels 

\/ Filled with Liquids Exchange their Contents. 

k!_J Two glasses, Fig. 43, of the same capacity and 

Fig. 43. Transfer of size of rim, are filled to the brim with liquids that 

Liquids. do not readily mix, say, one with water and the 

other with kerosene. 

Hold a card over the glass containing the denser liquid, invert it, and 

place it exactly above the other glass. Carefully slide the card to one 

side until a small segment of circle affords communication between the 

two vessels. The denser liquid passes down at one end of the segment 

and the rarer rises at the other end until the two liquids have completely 

changed glasses. By careful manipulation the card may be slid back to 



EXPERIMENTS 



95 



its place and the upper vessel replaced upon the table, the liquids having 
been interchanged without a third vessel. 

Experiment No. 20, Art. 32. N?s. 20 to 24, inch, Illustrate Surface Tension. 

In a bottle (Fig. 44), put a saturated 
solution of zinc sulphate, sp. gr. about 
1.4, to the depth of three or four centi- 
meters; on this, by means of a pipette, 
place about one cubic centimeter of car- 
bon bisulphide, sp. gr. 1.2Q, and carefully 
add water a few centimeters more in 
depth. The carbon bisulphide will as- 
sume a spheroidal form (if the globule is 
small it will be almost spherical), and 
will float between the solution and the water. 



A— Water 



B— Carbon 
Bisulphide 



C-nSolution of 
Zinc Sulph. 



Fig. 44. 



Experiment No. 21, Art. 52. 
Moisten a clean plate of glass with a thin film of water. If this film is 
touched with the end of a straw that has been dipped in sulphuric ether, the 
tension of the film is so weakened that the water is drawn back in every 
direction, leaving a circular spot comparatively dry. This action occurs 
owing to the vapor of ether even before the straw touches the* water. 

Experiment No. 22, Art. 52. 
A wire ring (Fig. 45) about five centimeters in diameter has suspended 
from it a thread with a loop at the end. If the ring be dipped in a soap 




Fig. 45. Tension of Soap Film. 

solution, it will be overspread by a film that supports the thread. By a hot 
wire puncture the film within the loop. The film without the loop contracts 
to its smallest area, which is reached when the loop incloses the largest 
area; the figure of largest area inclosed by a line of given length is a circle. 



9 6 



PROPERTIES OF MATTER; MECHANICS 



Moreover, since the tension across the thread is everywhere equal and 
everywhere perpendicular to the bounding line, the figure would be a circle. 
If soap films are formed on any wire frame and broken at one or more 
places, the remaining figure will always have that surface, however peculiar 
its shape, which has a smaller area than any other surface everywhere equally 
taut and bounded by the. same edges. Nos. 21 and 22 are readily projected 
on the screen by a lantern. 

Experiment No. 23, Art. 52. 

On the surface of clean water drop a few small pieces of gum camphor. 
The camphor dissolves unequally rapidly at various points and the tension 
of the film of water is weakened. The contracting film twitches the cam- 
phor around in an erratic manner. Like the water, the camphor must be 
clear of grease, — it must not be fingered. With a shallow vessel, this 
experiment is readily shown on the screen by a vertical projection apparatus. 

Experiment No. 24, Art. 52. 
In a beaker containing a small quantity of water place a few drops of oil. 
The addition of a large proportion of alcohol, with stirring, will reduce the 

sp. gr. until the oil will rest suspended in 
the body of the mixture. The oil will 
then form globules, each surrounded by a 
film in a state of tension, the film con- 
tracting to the smallest possible size to 
contain the oil inclosed by it. For a given 
volume the form with the smallest super- 
ficial area is that of a sphere; and, more- 
over, the coming to this form is an example 
of potential energy in the film reducing to 
a minimum. 




Experiment No. 25, Art. 53. Nos. 25 and 
26 Illustrate Capillarity. 

A fine tube ab, Fig. 46, with a bore, say, 
0.5 mm. in diameter, widens at b to a 
large bulb, say, five or six centimeters in 
diameter, and of length be about five 
centimeters, the lower continuation being 
too wide for capillary action, say, one 
centimeter or more in diameter. On dip- 
ping this tube into a vessel of water the 
latter rises in the fine tube about six centimeters by capillarity. If, now, 
the tube be gradually raised, the water at a sinks in the tube but continues 



Fig. 46. 



Supporting Action of 
Capillarity. 



• EXPERIMENTS 



97 



at the same height above dc, and presently the very narrow column in the 
tube is supporting the wider portion of liquid in the bulb between b and e, 
and will sustain it entirely above the level of dc if the height be is less than 
the original capillary column ba. When the apparatus has been raised 
until a line as ff reaches dc, then if bf is greater than the length of the 
column sustained by capillarity in ab, the liquid in ab sinks into the large 
bulb, and the contents of the latter return to the vessel until the liquid is 
at the same level within the bulb and without. 

Experiment No. 26, Art. 53. 

Exhibit or project upon the screen the form of liquid between two plates 
in wedge shape, Fig. 47. 




IUIIHUUIIIIIII/ 



Fig. 47- Rise of Liquid between Two Plates. 

Experiment No. 27, Art. 54. Expansive Force of a Gas. 

If an air-pump receiver with open top have a thin rubber sheet tied over 
the mouth, and the air be exhausted, the downward pressure of the atmos- 
phere is shown by the depression of the rubber cover until it may burst. 
On the other hand, if a wide-mouthed bottle be closed by such a rubber 
membrane, and placed under a bell-jar receiver, when the air is extracted 
from the latter the pressure within the bottle forces the rubber membrane 
outward. The point especially to notice in this is that the internal pressure 
was there before the removal of the external air as well as afterwards; the 
exhausting of the air from the receiver did not put any force into the bottle 
that was not there before. 



Experiment No. 28, Art. 55. Nos. 28 and 29 Illustrate Pressure of the 

Atmosphere. 

Fill a tumbler to the brim with water; hold a card closely upon the top 
of the glass and invert it. The card will be held against the glass by at- 
mospheric pressure, upwards or sidewise. Continue the experiment as de- 
scribed in Art. 55. 



9 8 



PROPERTIES OF MATTER; MECHANICS 



Experiment No. 2Q, Art. 53. 

Magdeburg hemispheres (Fig. 48) are two hollow hemispheres neatly 
fitted together, one of them having a stopcock by which it can be attached 
to an air pump. When put together with full air pressure within, they 
are easily separated, but when the air is exhausted they withstand a strong 
effort to pull them apart. The fact that this is true, no matter what may 





Fig. 48. Magdeburg 
Hemispheres. 



Fig. 49. Osmosis of Gases. 



be the position of the hemispheres, again illustrates the equality of fluid 
pressure in every direction. If, in this condition, they are placed under 
the receiver of the air pump and the air is exhausted from around them, 
they fall apart of themselves. 

Experiment No. 30, Art. 68. Osmotic Pressure. 
A closely sealed bottle B, Fig. 49, partly filled with colored water has 
an efflux tube A and another tube C leading from the upper part of B into 
the sealed porous cup P (a small new battery jar with a cork stopper that 
fits tightly and is well covered with sealing wax). The bell jar / is filled 
with illuminating gas by the tube T and is then placed to envelop P. The 
pressure due to the osmosis of the illuminating gas causes the liquid in B to 



EXPERIMENTS 99 

flow out through A . On the removal of /, the rare gas in P issues through 
the porous cup into the denser atmosphere, and the liquid in A runs back 
into the bottle. 

Experiment No. 31, Art. 68. Diffusion of Liquids. 

Put a solution of copper sulphate to the depth of five or six centimeters 
in a narrow glass vessel, and carefully add an equal depth of alcohol on top 
of the solution by letting it trickle down the side of the vessel from a pipette. 
Cover the vessel and set aside for several days where it will not be shaken. 
Observe the progress of diffusion. 



CHAPTER II. 

HEAT. 

70. Temperature. — Temperature is a term which is applied 
to a body to express that condition to which we ascribe the sensa- 
tions which we indicate by the terms hot, cold, warm, cool; and 
differences in which we signify by the various degrees of these 
adjectives, as hotter, colder, etc. But it is found that our sense 
of touch, or even our " temperature sense " as distinguished from 
the sense of touch, is often inadequate to distinguish correctly 
the changes in the condition of a body, or the difference of condi- 
tion of different bodies. And besides, we should have some way 
of expressing temperature in physical terms rather than physio- 
logical; for. our senses may so far deceive us as to make us feel 
cold and shiver when our temperature is above normal. So we 
can only proceed with the above idea of temperature temporarily. 

With a change of temperature in a body, other changes are 
observed to take place, the most common being, perhaps, a 
change in size; and it is found, furthermore, that under certain 
conditions a body always has the same size, and changes in size 
by the same amount between two of these so-called standard 
conditions. For example, any given mass of mercury, if placed 
in melting ice, will always increase in volume in the same pro- 
portion when transferred into water that is boiling under a 
pressure of one atmosphere. And so will any other substance 
which under these circumstances is continuous in its physical 
state, i.e., solid, liquid or gaseous. 

The temperature of melting ice, then, is considered constant 
in nature, and also that of water boiling under pressure of one 
atmosphere. The difference between these might be considered 
a unit difference of temperature, and the difference in size of a 
body, corresponding to this difference of temperature, might be 

100 



THERMOMETER SCALES IOI 

taken as the means of measuring various other differences of 
temperature. It is convenient, however, to use a smaller unit 
of difference of temperature, a fractional part of the difference 
between the above two standard conditions of freezing and boiling 
water. If the expansion of a substance, as mercury, between 
these temperatures, is divided into, say, ioo equal parts, one of 
these parts is taken to represent a unit change in temperature, 
which is called one degree (i°) Centigrade. It is at first only as- 
sumed that equal successive changes in the physical condition 
of the substance whose temperature is to be examined will be 
attended by equal changes of volume in the substance by which 
the temperature is being examined; but subsequent study of 
various substances shows that the assumption is correct within 
determinate limits, and what those limits are for different sub- 
stances. A substance, then, so prepared as to show its changes 
of volume exactly, becomes an instrument to measure changes 
of temperature, and is called a thermometer. But observe, it 
can only show differences in temperature, and in no wise tells 
temperature in an absolute sense; nor have we, up to this point, 
any meaning for temperature in that sense. 

71. Temperature Scales. — While the standard tempera- 
tures, and therefore the difference between them, are fixed in 
nature and are independent of our means of examining them, 
a degree of temperature may mean any fraction we please of 
this fixed difference; and, also, the same fraction may be appar- 
ently of very different size on different thermometers. 

72. Thermometer Scales. — The common scale for scientific 
use is that in which the temperature of melting ice. is marked 
zero, that of boiling water 100, and the range of temperature 
from freezing to boiling water is divided into one hundred equal 
parts or degrees. It is the centigrade scale. 

The common scale in domestic use in England and America, 
and also for engineering use in those countries, is the Fahrenheit, 
on which the temperature of melting ice is marked 32 and that 
of boiling water 212 ; while in Russia, and to some extent in other 
European countries, the Reaumur is used. For these refer fur- 



102 HEAT 

ther to elementary physics. (Exhibit the thermometer with no 
scale marked; is it then a Fahrenheit thermometer or a Centi- 
grade? How, when it has two scales?) 

All thermometers except electrical ones depend for their indi- 
cations upon expansion of bodies with rise of temperature and 
corresponding contraction on cooling. They may, therefore, be 
of solid, liquid or gaseous material. The actual measurement 
that is made in determining temperature is, then, of a length. 
Two fixed temperatures in nature are needed to get a correct 
scale, which is divided arbitrarily and the numbers themselves 
counted from an arbitrary zero. 

(Exhibit thermometers, solid, liquid, gaseous; maximum and 
minimum thermometers. Conditions of a good thermometer: 
in general, large change of volume per degree, promptness to 
change, wide range. Deep-sea thermometry, pyrometry, electri- 
cal determination of temperature change.) 

There are a few substances that act directly at variance with 
the law of expansion by heat; such are iodide of silver, India 
rubber, and some alloys. As such conduct, however, is anoma- 
lous, we need more particularly to examine that which is normal. 

Experiment No. 32, page 147. Gravesande's Ring. 

A bulb containing colored liquid shows expansion of liquid; and 
one containing air, the expansion of gas; the latter sensitive. 

After settling upon the freezing and boiling points of water 
for the fixed temperatures, and therefore definite points on the 
thermometer scale, the division of the scale intervening into one 
hundred parts seems natural enough; but it may seem singular 
that Fahrenheit should have marked those points 32 and 212 
respectively, dividing the intervening distance into 180 degrees; 
and that Reaumur should have used 80 divisions for the same 
range of temperature. 

Note. — Daniel Gabriel Fahrenheit, Danzig, Holland, 1686-1736. His early 
thermometers were of alcohol; he first solved the problem of temperature compari- 
sons by making thermometers that agreed with one another. Previously all appa- 
ratuses for the purpose were independent of one another and wholly arbitrary. 



THERMOMETER SCALES 103 

Fahrenheit made thermometers of alcohol as early as 1709 and did not know of the 
large coefficient of expansion of mercury and its suitability for such purposes until 
1 7 14. He employed various scales on his early instruments, his latest being the 
one now in common use and known by his name. Various statements have been 
made as to his choice of divisions, but all agree in his determination of the zero by 
a mixture of ice and salt, and which he called zero, as it was the lowest temperature 
reached in Holland in the unprecedentedly cold winter of 1709. He then marked 
on his thermometer the point of melting ice as 32 and that of the normal tem- 
perature of the human body as 96 . (Rosenberger, Geschichte der Physik, Vol. II, 
pp. 280, 281, no explanation being given as to the choice of numbers.) Fahrenheit 
simply determined the relative volumes of the mercury in his thermometer at his 
lowest temperature (zero), at the freezing of water, and at the boiling of water. 
These were found to be as the numbers 11,124, II > I 56, 11,336, showing at the same 
time that the mercury within that range expanded at uniform rate. Then, of his 
arbitrary unit volume, at freezing there were 32 more than at zero, and at boiling 
212 more. 

Reaumur introduced his scale in 1731, using spirits of wine of such strength that 
for a range of temperature as large as between the freezing and boiling of water 
1000 parts should expand into 1080 in bulk, dividing the interval into 80 parts. 
This is still used in Spain and Germany, and was the only one used in France prior 
to 1789. (Rosenberger, loc. cit.) 

The centigrade scale was introduced in 1742 by the Swedish philosopher Celsius 
at Upsala, and was established in France along with the metric system during the 
French Revolution, 1790. 

It is interesting to note that Fahrenheit in his experiments on thermometry 
learned of the variation of the boiling point of water, and recognized its connection 
with the atmospheric pressure, so that he proposed this use of the thermometer as a 
barometer. He thus anticipated, by a hundred years, Dr. Wollaston's hypsometer. 
(Rosenberger.) 

Mercury is applicable only between the temperatures — 34 C. 
and +35o°C; alcohol may be used as high as 78 C, and as 
low as — ioo° C. Alcohol begins to harden by getting pasty, 
but only at very low temperature ( — 129° C). Maximum and 
minimum thermometers; Breguet's metallic thermometer, coiled 
spiral of triple layer of metal, inner coil of silver (most expansi- 
ble), then gold, and outside is platinum (least expansible). Other 
common metal thermometers of two metals, the dial thermom- 
eters common in cars. Differential thermometer to show the 
fact of difference in. temperature, but not convenient for measur- 
ing. 

That solids have different rates (coefficients) of expansion is 
shown by compound expansion bar of brass and iron. 



104 



HEAT 



l: 



Experiment No. 33, page 147. Compound Metal Bar. 

Gridiron pendulum, coefficients of steel and brass are as 11 : 19. 
Attachments in gridiron are shown in Fig. 50, where the solid 
lines are steel and the open ones brass. 

Elongation downwards, (si + s 2 + s 3 )k 8 . 
Elongation upwards, (b ± + b 2 )k b ; putting 
these elongations equal to each other, we 
derive 

Si + s 2 + s s = kb = 19 ^ 

h + h ka II 

Mercurial pendulum, expansion of steel: 
apparent expansion of Hg as 1 : 14. 

Experiment No. 34, page 147. Trevelyan's Rocker. 

Experiment No. 35, page 148. Contraction of 

India Rubber. 

The promptness of expansion of metals is 
shown by Trevelyan's rocker. 

If a metal be compressed heat is de- 
veloped, i.e., given out, just as the appli- 
cation of heat to the metal resulted in its 
expansion. Also, if a wire be stretched and 
in consequence enlarged, it is more cold. The 
same applies to all substances which expand 
by being heated. It would then seem only consistent that a 
body which contracts by being heated should, in its turn, rise in 
temperature when expande d; and as India rubber does thus con- 
tract, it is interesting to note that it does give out heat when 
suddenly stretched. 

Electrical determination of temperature change. 
Coefficient of expansion : 

For solids: linear (a), superficial (2 a), cubical (3 a); 
For fluids : cubical (or voluminal) only. 
Correction of balance wheel of watch or chronometer. 
Difference between one degree Centigrade and one centigrade 
degree. 




Fig. 50. Gridiron Pen- 
dulum. 



NATURE OF HEAT 105 

Examples. — 

1. What temperature does a Fahrenheit thermometer indicate when a 
Centigrade thermometer reads o°, — 5 , 15 , 37. 8°, ioo°? 

Ans. To third, 59 . 

2. What is the temperature by the Centigrade scale when a Fahrenheit 
thermometer reads o°, — 5 , 32 , ioo°, 392 ? 

Ans. To second, — 2o|°. 

3. Show that — 40 represents the same temperature on both the Centi- 
grade and the Fahrenheit scale. 

73. Nature of Heat (sketched briefly) — "The theory sup- 
poses that the molecules of every body are in a state of per- 
petual agitation, and this may consist in the motion of the mole- 
cule as a whole, or as a vibration or rotation of its constituent 
parts, or both. This molecular motion is supposed to depend 
upon the temperature : the hotter a body is, the greater the in- 
tensity of its molecular agitation. In a solid the molecules are 
supposed to oscillate around mean positions. Each is confined to 
a very small space which it never leaves. As the temperature 
rises the molecular agitation increases, and at length becomes so 
violent that the molecules break away from their imprisonment 
and wander about indiscriminately amongst each other. In this 
state the substance is said to be in the liquid form. ... In 
order to endow the molecules with this extra motion, and also 
to overcome the forces which hold the molecules confined in the 
solid state, work must be done, and this work is the equiva- 
lent of what is known as the latent heat of fusion." Work is 
transference of energy. The body received energy in the form 
of heat, represented mechanically by the kinetic energy of all its 
molecules in the aggregate. The absolute energy is not deter- 
mined, but only the change of energy, as indicated by change of 
temperature when that is the only effect. Further heating raises 
the temperature, increases energy of molecules ; they finally break 
their bonds, and in gaseous form the energy due to gasifica- 
tion shows as pressure and temperature. (See Preston's Theory 
0] Heat, p. 66 and further.) 

Effects of heat (see Daniell's Physics, 1st ed., p. 322 to foot 
of p. 324, and from foot of p. 327 to middle of p. 328). 



io6 



HEAT 




Fig. 51. Apparatus to show Tern 
perature of Water at its Maxi 
mum Density. 



74. Anomalous Behavior of Water. — While substances usu- 
ally change continuously in the same way with change of temper- 
ature from the point of liquefaction 
to that of gasification, water is ex- 
ceptional, in that it first contracts 
on the application of heat until it 
reaches its smallest volume, and 
therefore its greatest density, and 
upon further rise of temperature it 
continually expands until it reaches 
a temperature where further appli- 
cation of heat converts the liquid 
into a gas. This temperature of 
maximum density is 4 C. or 39. 2 F. 
(Apparatus as in Fig. 51 requires 
constant filling up with freezing mix- 
ture (J coarse salt and § ice shav- 
ings) , and begin with water at about 
45 F. It is well to have apparatus filled and fitted before the 
lecture begins, as the progress of the experiment is slow.) 

All constants or peculiarities of water are important on account 
of its prominence in the economies of our daily lives. 

The consequence of the conduct of water as k cools to the freez- 
ing point is important and apparent to every one; the reason of 
it may excite very different feelings, as is strikingly presented 
in Professor Tyndall's Heat a Mode 0} Motion (pp. 109-111), here 
quoted. 

" Count Rumford was so impressed with the anomalous action of water 
that he devoted a whole chapter to speculations regarding it. 

"'It does not appear to me,' he writes, 'that there is anything which 
human sagacity can fathom, within the wide extended bounds of the visible 
creation, which affords a more striking or more palpable proof of the wis- 
dom of the Creator, and of the special care He has taken in the general 
arrangement of the universe to preserve animal life, than this wonderful 
contrivance.' Rumford's enthusiasm was excited by considerations like 
the following: Suppose a lake exposed to a clear wintry sky. The super- 
ficial water is first chilled; it contracts, becomes heavier, and sinks by its 



ENERGY IN A BODY IN DIFFERENT STATES 107 

superior weight, its place being taken by the lighter water from below. In 
time this is chilled and sinks in its turn. Thus a circulation is established, 
the cold dense water descending, and the lighter and warmer water rising 
to the top. Supposing this to continue even after the first pellicles of ice 
have been formed at the surface, the ice would sink, and the process would 
not cease until the entire water of the lake would be solidified. Death to 
every living creature in the water would be the consequence. But just 
when matters become critical, Nature, speaking poetically, steps aside from 
her ordinary proceeding, causes the water to expand by cooling, and the 
cold water to swim like a scum on the surface. Solidification ensues, but 
the solid is much lighter than the subjacent liquid, and the ice forms a pro- 
tecting roof over the living things below. 

" Rumford obviously regarded this behavior of water as a solitary ex- 
ception to the general laws of nature. 'Had not Providence,' he says, 
'interfered on this occasion in a manner which may well be considered as 
miraculous, the solitary reign of eternal frost would have spread on every 
side from the poles.' . . . 

"He begs the reader's candor and indulgence while he investigates the 
subject. ' I feel,' he says, ' the danger to which a mortal exposes himself who 
has the temerity to undertake to explain the designs of Infinite Wisdom.' 
But though he admits the enterprise to be adventurous, he contends that 
it cannot be improper." Professor Tyndall goes on to remark that "facts 
like those discussed by Rumford naturally and rightly excite the emotions. 
Indeed the relations of life to the conditions of life — the general adaptation 
of means to ends in nature — excite in the profoundest degree the interest of 
the philosopher. But in dealing with natural phenomena, the feelings must 
be carefully watched. They often lead us unconsciously to overstep the 
bounds of real knowledge, and to run into generalizations which are in per- 
petual danger of being overthrown. . . . Rumford was wrong in supposing 
that the case of water illustrated a miraculous interposition of Providence, 
for the case is not an isolated one." He then calls attention to an iron 
bottle, rent by the cooling of molten bismuth. "There is no life here to 
be saved, still the bismuth accurately imitated the behavior of water. Once 
for all it may be said that the natural philosopher, as such, has nothing 
to do with purposes and designs. His vocation is to inquire what Nature 
is, not why she is; though he, like others, and he, more than others, must 
stand at times rapt in wonder at the mystery in which he dwells, and towards 
the final solution of which his studies fail to furnish him with a clue." 

75. Energy in a Body in Different States. — Since heat is 
energy, it is apparent that a body when expanded by being heated 
possesses more energy than when contracted ; a given mass of any 



108 HEAT 

substance contains more energy when in liquid than when it is 
in solid state, and more when it is in gaseous than when it is in 
liquid state, if the change from one state to another in each case 
is due to addition or abstraction of heat. 

76. Absolute Zero. — While liquids, and especially mercury, 
are for many purposes convenient substances for a thermom- 
eter, gases are more accurate, especially when they are so rare 
as to conform closely to Boyle's law. A gas that exactly con- 
forms to this law is called a perfect gas, and air and the so-called 
permanent gases are approximately such. 

A given mass of such gas at o° C. and under constant pressure 
changes in volume 2^3- for a change of i° C. in temperature. 
This fraction 0.003665 is practically constant for a wide range 
of temperature and is called the coefficient of expansion for 
gases. Also, if the volume were held constant, it is found that 
the pressure varies in the same proportion per degree centigrade. 
If this proportional change held good indefinitely, then at — 273 , 
or at 2 73 below the temperature of freezing water, the gas, if 
kept at constant pressure, would shrink to nothing, or if kept 
at constant volume would lose all pressure. The first of these 
is inconceivable and the latter has not been realized; but this 
theoretical value ( — 273 C.) is called the absolute zero, and 
serves as a starting point from which to reckon all temperatures 
on an absolute scale, although it is known that gases change their 
rates of contraction (or expansion) , and many of them their states 
from gaseous to liquid, before they reach so low a temperature. 

Now if temperatures are measured from this absolute zero, the 
pressure varies as the temperature. But we have seen (Art. 66) 
that when the number of molecules per unit of volume is con- 
stant, which is the case when the volume of a given quantity 
(mass) of the gas is constant, the pressure varies as the average 
energy per molecule. 

Again, if we mix two gases, they come to the same tempera- 
ture, and from mathematical principles the average energy for 
each set of molecules is the same. But in each case the energy 
is proportional to the common temperature; hence, whether we 



HEAT AND TEMPERATURE DISTINGUISHED 109 

take the same or different gases, the average energy of the mole- 
cules is proportional to the absolute temperature, or (8) "the 
temperature of a gas is proportional to the average energy of the 
molecules" (Wormell's Thermodynamics, p. 160). 

This being so, the temperature may be regarded as an expres- 
sion of the average energy per molecule, and it is so regarded for 
liquids and solids as well as for gases. Then, naturally, we see 
that the heat of a body is the total kinetic energy of its molecules, 
and these may be taken as the strict physical meanings of the 
two terms " heat" and " temperature." 

77. Avogadro's Law. — Since for a gas of given temperature 
p =\ NmV 2 , where N is the number of molecules in a given 
volume, and m the mass of a molecule, if we have equal volumes 
of two gases at the same pressure and temperature, 2Vi and Wi 
being the number of molecules and the mass of a molecule of one 
gas, and N 2 , nh the corresponding quantities for the other gas, 
then, since both have the same pressure p, 

i NmiV? = i N 2 m,V 2 \ 

If these gases are mixed in a vessel of double the volume of each 
gas, the pressure will remain the same, the temperature does not 
alter, the product of pressure and volume for each gas is the same, 
and therefore the kinetic energy, or 

iwiTV = %m 2 V 2 2 . 

These, substituted in the above equation, give iVi = N 2 ; that is, 
any two gases having the same temperature, pressure and volume 
contain the same number of molecules. 
This is the law of Avogadro. 

78. Density Not Determined by Closeness of Molecules. — 
Here we see the reason for rejecting the idea that by density 
of a substance we are to understand the closeness of arrange- 
ment of its molecules. Equal volumes of two gases, say oxygen 
and hydrogen, at the same temperature and pressure would 
contain an equal number of molecules ; on the average the mole- 
cules of the two gases would be equally separated, but we would 



HO HEAT 

not say the two gases were of equal density. Since their masses 
would be in the ratio of 16 : i, so would their densities. 

79. Work of Expansion of a Gas; Combined Relation of 
Pressure, Temperature and Volume. — Suppose a mass of gas 
to be inclosed in a cylinder, stopped by a gas-tight, freely moving 
piston, whose cross-section has an area A. If p is the pressure 
per unit area against the piston, the total pressure is pA . With 
this pressure constant, if the gas is heated it will expand and 
move the piston a distance /. The work of doing this is pA X /, 
and if we suppose the material of the cylinder to be unaltered 
in dimensions by the heat, this quantity pAX I is the work of 
expanding the gas. But pA X I = p X At, and Al is the volume 
moved through by the piston, or the increase in volume of the gas. 
Thus the work of changing the volume of a gas is found by multi- 
plying the change in volume by the pressure per unit area. If 
volume is cubic centimeters and pressure is dynes per square 
centimeter, work is ergs. 

According to the law of Charles, if the volume of a given mass of gas 
is constant, its increase of pressure is proportional to the rise of tempera- 
ture; and by the law of Mariotte, with constant pressure the increase of 
volume is proportional to the rise of temperature, — in each case 2T3 of the 
pressure or volume at o° C. Then, if we could reckon temperature from 
an absolute zero, each quantity, pressure p and volume v would vary as 
the temperature T, or pv = RT, where R is a constant depending on the 
units for p, v, and T. (This quantity R is sometimes called Regnauit's 
constant.) Since this equation would be true for all temperatures, it would 
be good for the temperature o° C, for which T = 273 °; then, if p , v , 
are the pressure and volume of a gas at o° C, 

PoVo = R-(2 73 ) or R = ^. 
273 
Under the kinetic theory of gases we see that pv = const. X temperature, 
and, by the experimental laws of Charles, Mariotte, and Boyle, we have 
here the means of determining the Const. R, and of expressing the second 
member of this equation numerically. If p = the pressure of one at- 
mosphere in dynes, i.e., 1,013,250 (p. 82, foot-note), and v = volume of one 

-r, 1,013.250 X 22,400 
gram-molecule of gas, i.e., 22,400 c.c, R = = 8.3 X io 7 . 

This value of R is sometimes called the universal gas constant. This is in 
terms of work units, ergs. For its value in heat units, see Ex. 6, p. 145. 

Examples. — 

1. The density of dry air at o° and 76 cm. barometer pressure is 
0.001293 g./c.c. Show that the density at 76.8 cm. pressure and 15 C. is 
0.001239 g./c.c. 



SPECIFIC HEAT III 

2. A mass of gas was cooled from ioo° C. to 15 C. under constant pres- 
sure, and its volume was then 150 c.c. What was its original volume? 

Ans. 194.27 c.c. 

3. 1000 c.c. of air at standard atmospheric pressure and o° C. is heated 
to ioo° C, the pressure remaining constant. What is its increase in volume, 
and how much work was done in expanding? 

Ans. 366.3 c.c; 371 X io 6 ergs. 

80. Calorimetry; Unit of Heat. — With a given substance 
under given conditions, it is found that the same amount of 
heat (obtained by energy of mechanical action, or chemical 
action, or any other determinable means) produces the same 
change of temperature. Hence the unit by which to measure 
heat may be fixed by a temperature change in some standard 
substance. For measuring directly, a unit is generally of the 
same nature as the quantity to be measured; e.g., the unit to 
measure duration is itself a period of time; to measure distance, 
a length; etc. To measure heat, the unit is a quantity of heat. 
The c.g.s. unit of heat is the quantity of heat that will raise one 
gram of water from o° to i°C. in temperature. This unit is 
called a calorie (or sometimes a water-gram-degree). The Brit- 
ish thermal unit (B.T.U.) is the heat required to raise one pound 
of water i° F. in temperature. 

81. Capacity for Heat. — By the capacity of a body for heat 
is meant not the quantity of heat it can contain, but the quan- 
tity of heat required to raise the temperature of the body one 
degree. 

82. Specific Heat. — By this is meant the quantity of heat 
required to raise a given mass of any substance one degree in 
temperature compared with the amount of heat needed to raise 
an equal mass of water through the same temperature change. 
For water this is unity, and, as compared with water, the specific 
heat of any substance will be the ratio of the heat per gram to 
the change of temperature; i.e., it is numerically equal to the 
number of calories required to raise one gram of the substance 
one degree Centigrade. The specific heat of water is very nearly, 
but not quite, constant from o° to ioo°, decreasing slightly from 



112 HEAT 

o° to 37 , and then slightly increasing. Measurement of heat is 
calorimetry. The commonest method of determining the specific 
heat of bodies is called the method of mixtures, though there are 
various other methods in use. The method of mixtures proceeds 
on the assumption that if two substances at different tempera- 
tures are mixed, then, if there is no chemical action involved, the 
heat that is lost by one is gained by the other as they come to a 
common temperature. If one of the substances is a standard, as 
water, the heat it gives out in a known rise or fall of temperature 
is simply the mass of water multiplied by the number of degrees 
it was changed in temperature; and this is the heat that pro- 
duced the corresponding change of temperature in the other sub- 
stance. 

For a metal ball as an example : 
Let sp. ht. = c; 

Temperature of substance = T (say, ioo°) ; 

Temperature of water = / (say, 20 ); 

Temperature of mixture = 6 (say, 23 ) ; 

Mass of substance = M (say, 200 g.) ; 

Mass of water = m (say, 300 g.). 

Then heat gained by water is m {6 — t) ; 

Heat lost by substance is cM(T — 6). 
Equating these, we get 

m(0 -t) 
C M(T - 6) ' 

Using the above quantities, we should find c = 0.0584, which 
is approximately the value for tin. 

Experiment No. 36, page 149. Specific Heat and Capacity for Heat. 

Examples. — 
1 1. 520 g. of water cools from 15 C. to 4 C. How much heat does it lose? 

Ans. 5720 calories. 
2. A coil of copper wire at a temperature of 99.6 C. and weighing 180.4 g. 
is dropped into 240 g. of water at io° C. The copper and water come to a 
common temperature of 16 C. Find the specific heat of the copper. 

Ans. 0.0955. 



LATENT HEAT OF FUSION 113 

3. How much heat is required to raise the temperature of 416 g. of copper 
50 centigrade degrees? Ans. 1988 calories. 

Note. — In actual determination of sp. ht., the calorimeter (i.e., the vessel con- 
taining the water) undergoes the same change of temperature as the water in it, 
and in its capacity for heat it corresponds to a definite amount of water. This 
is called its water equivalent, and equals as many grams of water as the number 
of calories required to raise its temperature one degree. This must be added to 
the water placed in it, to get the equivalent mass of water actually heated or 
cooled. 

4. A piece of silver weighing 25 g. was heated to ioo° C. and dropped 
into a calorimeter containing 100 g. of water, the temperature of which was 
raised from n° to 12.2 . The water equivalent of the calorimeter, stirrer 
and thermometer was 4.5 g. What was the sp. ht. of the silver? 

Ans. 0.057. 

5. What is meant by the statement that the sp. ht. of water is thirty 
times the sp. ht. of mercury? 

83. Latent Heat of Fusion. — When a body begins to melt, 
the further application of heat does not cause any further rise 
of temperature in the mixture of solid and liquid until the former 
is all melted. The heat that is thus added to accomplish the 
liquefaction has been called the latent heat of fusion, and is again 
given out if the body returns from the liquid to the solid state. 

The method of mixtures enables us to determine the latent 
heat of water or the latent heat of fusion of ice. By melting a 
known mass of ice at o° in a known mass of water at t°, if the 
temperature of the mixture is 6°, then the water in cooling has 
given out heat that has melted the ice and raised the tempera- 
ture of the water, resulting from the melting of the ice from 
zero to 0°. 

For example, suppose 50 g. of ice is introduced into 200 g. of 
water at 6o° C, and the resulting temperature, when the ice is 
melted, is 32 C. Call latent heat of water, L. 200 g. of water in 
cooling from 6o° to 32 , i.e., through 28 , gives out 200 X 28, or 
5600 calories; of this, it required to raise the 50 g. of melted ice 
from o° to 3 2 , 50 X 32, or 1600 calories; the remaining 4000 
calories were expended in melting the 50 g. of ice; therefore, the 
number of calories required to melt one gram of ice is --5-5--, 
or 80 calories, which is the latent heat of fusion of ice. If heat is 



It4 HEAT 

energy, what has become of the energy when the heat is thus said 
to be latent? 

84. Freezing (or Solidifying) is a Warming Process. — As heat 
is absorbed in the conversion of a solid into a liquid, so the 
change of a liquid into a solid is attended by the liberation of 
heat. For every gram of water that changes into ice at o° C, 
80 calories are set free and tend to warm the vessel or surround- 
ing atmosphere. This delays the progress of freezing and may 
prevent the air from becoming so cold as to injure fruits or 
vegetables. Where such articles are stored in bins, advantage 
is sometimes taken of this fact when a severe fall of temperature 
is impending, by placing vessels of water offering a large surface 
in the vicinity of the articles that would be injured by the severe 
frost. The danger is mitigated by the heat liberated when the 
water freezes. 

Examples. — 

1. How much heat will be absorbed by 550 g. of ice in melting? How 
much heat will be given out by 880 g. of water in freezing? 

Ans. 44,000 cals.; 70,400 cals. 

2. How much water at 98 C. would be required to melt the 550 g. of ice 
in Example 1? . Ans. 449 g. 

3. Find the result of mixing 1 kg. of snow at o° C. with 4 kg. of water at 
30 . Ans. 5 kg. of water at 8° C. 

4. What will result if 2 kg. of boiling water is poured on 2.5 kg. of snow 
at o° C? 

85. The Two Specific Heats of a Gas. — With a given mass 
of gas so inclosed as to permit no expansion, the heat neces- 
sary to raise its temperature is all expended in increasing the 
kinetic energy of the molecules. The volume will be constant, 
but the pressure will increase with rise of temperature. The 
amount of heat needed thus to raise the temperature of one gram 
of gas one degree is called the specific heat at constant volume. 

If the gas is free to expand as it is heated, it will push back its 
inclosing walls a certain distance with a force equal to the ex- 
ternal (constant) pressure, thus doing work; and, in addition to 
this, the mean kinetic energy of the molecules is to be increased 



CHANGE OF STATE 1 15 

as much as in the other case, for the same rise of temperature. 
In a gas thus heated, more heat is required per degree rise of 
temperature, and the heat needed thus to raise one gram of gas 
one degree in temperature is called its specific heat at constant 
pressure. 

The latter is comparatively easy to determine directly; the 
former is difficult to determine directly, but, from known thermo- 
dynamic principles, it can be derived from the velocity of sound (!) 
in a gas at given pressure. This will be explained later. (See 
Watson, Arts. 204, 205 and 215.) 

86. Change of Specific Heat with Change of State. — While 
the specific heat of most bodies is slightly different at different 
temperatures, the difference in specific heat of a substance in the 
various states of aggregation is considerably greater than it is for 
mere differences of temperature, and usually it is highest for the 
liquid state. For example, for water we find, solid, 0.50; liquid, 
1.000; gas, 0.477. (See Watson, Art. 206.) 

Dulong and Petit's law is that the product of the specific heat 
of an element in the solid state into the atomic weight is a con- 
stant. It is found, also, that the product of the atomic weight 
into the specific heat of a gas is approximately constant, and about 
half the value of the product in the case of solids. For solids 
the product is about 6.4, and for gases about 3.4. This product, 
called the atomic heat, varies considerably for a supposed con- 
stant, but it is pointed out that the specific heat of most solids 
seems to become constant near a certain temperature, and if the 
specific heat at this temperature were employed for getting the 
atomic heat the results would more nearly verify Dulong and 
Petit's law. (Watson, Art. 207.) 

87. Change of State ; Melting Point; Laws of Fusion. — The 
passage of a substance through the various states, solid, liquid 
and gaseous, together with the changes of energy involved, has 
been indicated in Arts. 73 and 75. 

(a) For each substance there is a definite temperature at 
which the change of state occurs, that at which it changes from 
solid to liquid being known as its melting point. 



Il6 HEAT 

(b) When the melting point has been reached, no further rise 
of temperature occurs by application of heat until the body is 
all melted. 

Some substances, as wax and wrought iron, first become 
plastic, in changing from solid to liquid, and the exact melting 
point is hard to fix upon, since the real condition of liquidity is 
vague. 

88. Influence of Pressure on Melting Point. — As will be 
pointed out later, when the boiling point of a substance is 
designated, it is necessary to specify the pressure under which 
boiling (or vaporization) takes place. For the other standard 
temperature, viz., that of exchanging liquid and solid states, it 
is usually not necessary thus to specify the pressure. Strictly 
speaking, however, the temperature at which this change of state 
occurs does depend somewhat on the pressure, and it varies in 
different measure with different substances. 

It is readily seen that if a body contracts in melting, then the 
effect of applying pressure is to assist in diminishing the volume, 
and the substance more readily liquefies. That is, it will not 
remain in the solid state at the temperature at which it would 
have so remained if it had not been compressed; therefore, to 
keep it frozen under pressure it would have to be colder, or, the 
melting point is lowered by pressure. With bodies that expand 
on melting, the application of pressure makes it more difficult for 
them to melt, and they must be made hotter than would other- 
wise be necessary, or, the melting point is raised by pressure. In 
any case the change of temperature is very small even for a great 
pressure. 

Water is a substance whose freezing point is lowered by pres- 
sure, the lowering amounting to 0.0076 per atmosphere, which 
does not continue in direct proportion to increase of pressure, 
but under 13,000 atmospheres a freezing point of water as low 
as — 18 has been reached. 

Faraday discovered that when two pieces of melting ice are 
pressed together they freeze together. This phenomenon, which 
is illustrated in various ways, is called regelation. By suspend- 



INFLUENCE OF PRESSURE ON MELTING POINT 117 

ing a heavy weight from a fine wire that passes over a block of 
ice — the pressure under the wire is great — the ice melts, heat (of 
fusion) is absorbed from the wire and the neighboring ice, and 
the wire sinks in the block. The cold water passes above the 
chilled wire and, with the pressure released, it again freezes 
solidly with the ice on each side. 

Experiment No. 37, page 149. Regelation. 

A block of ice five or six cm. square in cross-section, under a 
fine piano wire carrying fifteen pounds, will be cut through in 
from twenty to thirty minutes. 

Professor Tyndall has shown that the movements of glaciers 
may be explained, perhaps, better on the basis of regelation than 
on that of viscosity. 

Philosophy of making a snowball : Very cold snow is not good 
for snowballs, for pressure cannot be applied great enough to 
lower the melting point below the temperature of the snow, and 
regelation will not occur; but with snow at o° it is precisely the 
regelation that makes the firm ball. So, too, with a heavy cart 
leaving a frozen track after the passage of the wheels. 

The converse of this principle of regelation leads to some 
interesting deductions. Just as those solids which contract on 
melting take a lower temperature for melting under increased 
pressure, so those which expand upon melting, i.e., those whose 
density diminishes and which therefore sink in the liquid, re- 
quire a higher temperature for melting when the pressure is in- 
creased. "Thus we can understand why it is that the materials 
forming the interior of the earth are practically rigid and per- 
haps solid, though at a temperature far above their ordinary 
melting points." There is little doubt that a few hundred miles 
below the surface of the earth the temperature is far above the 
melting point of lava; it is equally well shown that the earth as 
a whole is nearly as rigid as a globe of steel of the same size. 
These two apparently inconsistent conditions are at once recon- 
ciled if we suppose the average materials of the earth to be such 
as, like lava, expand on melting. They may remain solid even 
above a white heat, for " if the earth were liquid throughout and 



Il8 HEAT 

of uniform density equal to its present mean density, the pres- 
sure within a few hundred miles of the surface would increase 
at the rate of somewhere about 800 atmospheres (or nearly 5! 
tons per sq. in.) per mile of depth ' 1 (Tait, Heat, pp. 124, 125). 

It is interesting to note the effect of pressure in the opposite 
direction. It is a familiar fact that various substances vaporize 
directly from the solid state without passing through the liquid 
state (as when clothes " freeze dry " in an atmosphere below 
freezing). Camphor, arsenious acid, snow, are well-known in- 
stances. As a result of various investigations by himself and 
others, Dr. Thomas Carnelly in 1880-81 announced as a general 
proposition: {C In order to change a solid body into a liquid, the 
pressure upon it must exceed a certain amount, which may be 
called the critical pressure, and below which the substance will 
not melt, no matter how great heat be applied to it " (Rosen- 
berger, III, 2, p. 658). This pressure is not to be confounded 
with the pressure of a gas at the critical temperature. It is 
evidently a very low pressure for all ordinary solids. Carnelly 
found it to be 420 mm. for chloride of mercury, and 4.6 mm. for 
ice. Above this pressure ice will melt by applying heat; below, 
it passes into vapor by sublimation. (See also Watson, Art. 223.) 
He also asserts that if the pressure can be kept low enough and 
the heating done rapidly enough (i.e., to prevent the formation 
of vapor which would raise the pressure), ice can be heated far 
above the boiling point of water, even as high as 180 C. (Rosen- 
berger, loc. cit.) 

The passage of a solid directly into vapor without becoming 
liquid is called sublimation. On this subject see Preston, Theory 
of Heat, Art 170; and Barker, p. 309. 

The freezing point, then, under one pressure may be higher 
than the boiling point under another pressure. For example, 
benzene, which is liquid at ordinary temperatures under atmos- 
pheric pressure, and will freeze in a vacuum at a temperature of 
5. 3 C, will boil under a pressure of one atmosphere at 8i°, but 
will freeze at 81.4 under a pressure of 3500 kilograms per sq. cm. 
or 3387 atmospheres. 



ELASTIC FORCE OF VAPORS 1 19 

89. Elastic Force of Vapors. — In passing from a solid to a gas 
a body generally goes through an intermediate liquid state; if not, 
the process is called sublimation. The change of a liquid to the 
gaseous state is vaporization. 

A liquid introduced into a vacuum vaporizes instantly, so 
much of it passing into vapor in the inclosed space as to exert a 
definite pressure. 

Experiments Nos. 38 and 39, page 150. Vapor Pressure. 

By introducing small quantities of liquid into the space above 
the mercury column of several barometer tubes and noting the 
depression of the column, it is seen that at the same temperature 
the vapors of different liquids have different elastic forces. 

A vapor denotes a substance in the gaseous form which, at 
ordinary temperatures, appears as a liquid or solid, while a gas 
denotes a substance which under ordinary circumstances appears 
in the gaseous form and which can only be reduced to the solid 
or liquid form by considerable pressure or lowering of tempera- 
ture. Those vapors which are on the point of condensation are 
called saturated vapors, while those which can suffer a certain 
amount of compression or cooling without condensation are called 
unsaturated vapors. In this sense all gases are unsaturated 
vapors, for they can all be condensed by the simultaneous applica- 
tion of sufficient cold and sufficient pressure. (Daniell's Physics, 
p. 205.) In some cases a vapor condenses directly into a solid, 
e.g., arsenious acid. (Ibid.) 

There are three processes of vaporization: (1) evaporation, 
where a liquid is converted into a gas quietly and without forma- 
tion of bubbles; (2) ebullition, where bubbles of gas are formed 
in the mass of the liquid itself; (3) vaporization in the spheroidal 
state, where a liquid evaporates slowly, although apparently in 
contact with a very hot substance. While the first mode is being 
exemplified continually, we can do little to illustrate it just now 
in the lecture room; but we may state the relations of vapors and 
their pressures (or tensions) according to Dalton's laws. 

I. "In space destitute of air the vaporization of a liquid goes 
on only until the vapor has attained a determinate pressure depend- 



120 HEAT 

ent on the temperature, so that in every space void of air determinate 
vapor pressure corresponds to determinate temperature.'' 1 

In the above experiment an attempt to reduce the space con- 
taining the saturated vapor will not increase the pressure but 
will result in condensing more vapor into liquid; to warm the 
vapor will increase the pressure. The pressure of a saturated 
vapor is called its maximum pressure (or tension) for that tem- 
perature. At 20° C. the maximum vapor pressure of 

mercury = 0.021 mm. of mercury column; 
water = 17.39 " " 
alcohol = 44.48 " " 
ether =433.26 " " 

II. "In a space filled with air the same amount of liquid evapo- 
rates as in a space destitute of air, and the same relation subsists 
between the temperature and pressure of the vapor whether the space 
contain air or not " 

This principle is involved in hygrometry, which we shall con- 
sider later; but, although unsaturated vapors obey Boyle's law, — 
and this law of Dalton's is equivalent to saying that the pressure 
of a mixture of vapors is the sum of the pressures due to each 
constituent as if the others were not present, — still this is found 
to be true only when the vapors are not very near saturation. 
"It would seem a priori that Dalton's law can only be an ap- 
proximation, for otherwise it would mean that by introducing a 
sufficiently large number of different kinds of liquids into the same 
space we could produce as great a pressure as we please, a result 
that is unlikely to be true " (Watson, Art. 219). 

90. Ebullition. — The layers of liquid first heated form vapor, 
which is condensed by the colder upper strata through which 
they rise. This rapid condensation of bubbles causes the singing 
of liquids before they boil. When the bubbles reach the surface 
ebullition has begun. The temperature of ebullition is depend- 
ent upon (1) external pressure, (2) nature of the vessel, (3) sub- 
stances dissolved in liquid, (4) nature of liquid. The last two 
we need not discuss here at all; the second, only to call attention 



EFFECT OF PRESSURE 



121 



to the fact that although the boiling water may differ in tempera- 
ture in different vessels the steam will be of the same temperature 
if the pressure is the same. Therefore we give especial atten- 
tion to the effect of pressure upon the boiling point of water. 

91. Effect of Pressure upon the Boiling Point of Water. — 
The pressure of vapor during ebullition equals the external 
pressure, for in the apparatus shown in Figure 52 the mer- 
cury stands at the same level in the arms 
a and b. (This is true, no matter what 
liquid is in the vessel.) The temperature, 
then, will continue to rise until that point 
is reached for which the corresponding vapor 
pressure is equal to the external atmospheric 
pressure (or superincumbent pressure from 
whatever source; perhaps the pressure of its 
own vapor if inclosed as in a boiler) . If this 
pressure is small, then the boiling point will 
be low; if great, the boiling point is high. 
Accordingly, as the barometer shows that 
the pressure of the atmosphere varies, the 
boiling of water under atmospheric pressure 
does not always occur at the same temper- 
ature. Furthermore, the temperature of 
ebullition being determined or the law of its change being 
determined, experimentally, as also the variation of elevation 
above sea level for a given change in barometer, a sensitive 
thermometer becomes available as a barometer. Such an instru- 
ment is called a hypsometer. This use of the thermometer is 
attributed to Wollaston, about 1800, but Fahrenheit had already 
suggested it as early as about 1700. We may use the term 
"boiling point " for any liquid, but when used without qualifica- 
tion it is usually with reference to water, and, in any case, it 
varies with the pressure. 

"A liquid boils or passes into vapor at a temperature at 
which the pressure of its saturated vapor is equal to that which 
the liquid supports. If now the pressure of the vapor of any 




Fig. 52. Pressure of 
Steam equals that of 
Atmosphere. 



122 HEAT 

substance at the freezing point is equal to or greater than one 
atmosphere, then this substance will not exist under atmospheric 
pressure in the liquid state, for as soon as the solid melts the 
liquid will pass off into vapor. Boiling will thus occur, as it were, 
at the surface of the solid. This will always occur at a given 
temperature if the pressure is less than that of the saturated 
vapor of the substance at that temperature; but if the pressure 
be greater than this value, the liquid form will be possible, and 
melting will occur if the given temperature is above the freezing 
point. Thus arsenic volatilizes without melting under the at- 
mospheric pressure, but if the pressure is increased, fusion may 
be effected; and Carnelly showed that ice, mercuric chloride and 
camphor do not melt below a certain pressure peculiar to each 
substance, and which he proposed to call the critical pressure," 
as we have mentioned before. (Preston, Theory of Heat, Art. 
170.) The volatilizing point of a solid under a given pressure 
is the maximum temperature at which it will remain in the solid 
state under that pressure. 

A liquid, then, may boil at any temperature, depending on the 
pressure it supports, but when not otherwise stated the boiling 
point means the temperature of boiling under the pressure of one 
atmosphere, i.e., 76 cm. of Hg. In this restricted sense the tem- 
perature of boiling is not the same thing as the boiling point. 
The boiling point, in this sense, of water, air and other substances 
is given in Art. 94. 

Experiments Nos. 40 and 41, page 151. — To set Water to Boiling by 

Cooling It. 

Culinary paradox: Show renewal of boiling in a flask when 
superincumbent vapor is partly condensed, by application of cold 
water or ice. Also, partially exhaust the air of a receiver 
covering a beaker of warm water (say 6o° or 8o°), and have 
some water initially at the same temperature standing in a 
vessel outside the receiver; compare the temperature of the 
water in the two vessels after boiling that under the receiver. 
Also, ether under the exhausted receiver will boil at ordinary 
temperature. 



LATENT HEAT OF VAPORIZATION 123 

These experiments show that water will boil at less than ioo° 
if pressure is diminished below 76 cm. For higher pressures the 
temperature of the vapor and of the water rises, the increase 
being one degree C. for about 27 mm. added pressure at first. 
With an addition of eight atmospheres of pressure (about 120 
pounds gauge), the temperature rises to 175 C. Papin's di- 
gester, with the safety valve which is used in the same form 
to-day, was described by their inventor, Denis Papin, in 1681. 
(When water is boiling it can be made hotter only in case greater 
pressure is put upon it.) 

When vapor is produced a certain quantity of heat is required 
to convert the liquid into vapor of the same temperature, which 
is then said to be latent heat; and if heat is available from no 
extraneous source, it must be supplied by the substance from 
which evaporation is going on, and its temperature will then fall. 
Water may thus be frozen by its own evaporation. If the evapo- 
ration takes place rapidly under very low pressure, it may freeze 
while boiling! 

Vaporization, then, absorbs energy and is a cooling process. 
That the cooling of a liquid due to its evaporation is in accord 
with the kinetic theory is shown thus: The temperature repre- 
sents the average kinetic energy of the molecules ; in evaporation 
only those molecules escape whose kinetic energy is above the 
average; consequently the average of those remaining is di- 
minishing and the temperature falls. (Hastings and Beach, 
Art. 171.) Local anesthesia by evaporation of ether, etc. 

92. Latent Heat of Vaporization. — When a liquid is brought 
to the point of boiling under a given pressure, a definite quan- 
tity of heat is required to convert a unit mass of the liquid 
into vapor at the same temperature. This is called the latent 
heat of vaporization. It varies with the temperature at which 
vaporization is effected. With water, starting at o° C, the total 
quantity of heat required to raise a gram to a temperature f and 
convert it into vapor at that temperature is expressed by the 
formula : 

H = 605.5 + °-3°5 *• (See Hastings and Beach, Art. 168.) 



124 HEAT 

This would give as the total heat of steam at ioo°, 636 calories, 
and for the latent heat at ioo°, 536 calories. Latest determina- 
tions give for the heat of vaporization, i.e., the latent heat at any 
temperature, L t = 596.73 — 0.601 / (Watson, Art. 214), which at 
/ = ioo°, becomes L = 536.63. Conversely, condensation gives 
out heat; hence, philosophy of steam heating. 

Experiments Nos. 42 and 43, page 152. Freezing Water by Evaporation. 

Cryophorus: Freeze water in a warm atmosphere by its own 
evaporation. Call attention to the necessity for a very perfect 
vacuum in the cryophorus. When the temperature has fallen 
to zero, further evaporation can only occur (since the vapor would 
become saturated) if the pressure over the liquid is less than 
4.6 mm.; also, if the temperature is to fall, heat must be taken 
from the water faster than it is supplied to it from the room. 
By evaporation of very volatile liquids intense cold may thus 
be produced. By the use of liquid sulphurous acid, or of liquid 
carbon dioxide, mercury may be frozen. When that process is 
applied at any particular place on the body, that spot may be 
so benumbed by the cold as to be insensible to pain, and minor 
surgical operations may be performed with the aid of such local 
anesthesia. 

Examples. 

1. What is meant by saying that the latent heat of steam is 536? How 
much heat is required to change 97 g. of water at ioo° C. into steam at the 
same temperature? Ans. 51,992 cals. 

2. How much heat is required to raise 100 g. of water from o° C. to 99 C. 
and convert it into steam at that temperature? (Art. 90.) 

Ans. 63,569.5 cals. 

3. How much heat is required to raise one gram of ice from — 20 C. to 
o° G., melt it, heat the water to ioo° C, vaporize it, and heat the steam to 
180 C? Ans. 764.4 cals. 

93. Internal Work and External Work in Heating a Body. — 

Except where a change of state is about to occur, we may re- 
gard the application of heat to a body as resulting in three kinds 
of changes : 



CRITICAL TEMPERATURE OF A GAS 125 

(1) Rise of temperature, — an increase in the average molec- 
ular kinetic energy. 

(2) Expansion, — an increase in molecular potential energy, 
since the positions of equilibrium for the oscillating molecules are 
forced farther from one another. (Counts for nothing in a gas.) 

(3) Pushing back the medium exerting pressure on the body, 
in expanding. 

(1) and (2) are called " internal work," (3) is " external work." 
In a change of state usually a considerable amount of energy is 
required or else liberated. Water could be represented in a rising 
scale of energy by ice, water, steam. 

94. Critical Temperature of a Gas. — The conversion of a 
gas into a liquid, as we have seen, may be effected at various 
temperatures, depending on the pressure. Whenever the pres- 
sure exceeds the maximum vapor pressure for the given tempera- 
ture, liquefaction ensues. This pressure is higher the higher the 
temperature, but for every gas there is a temperature above 
which no pressure will accomplish liquef action. This tempera- 
ture is called the " critical temperature." The pressure to 
produce liquefaction at the critical temperature is sometimes 
called the " critical pressure." Below this temperature, then, 
a body may be liquid or gas indifferently, or a given mass may 
exist at the same time partly in the liquid form and partly 
in the gaseous. The critical temperature for some gases is 
high, that of water being 365 ° C, at which temperature a pres- 
sure of 200 atmospheres is necessary for liquefaction, and 
above which no pressure will liquefy it. (If we lived normally in 
a temperature above 3 65 °, we would know nothing of liquid water, 
and would consider steam a permanent gas, as we have been wont 
to consider air.) Such is our situation relative to oxygen and 
various other gases. For oxygen the critical temperature is 
— 118 under a pressure of 50.8 atmospheres, although it will be 
liquid under one atmosphere pressure if its temperature is 
reduced to — 181 , and that is said to be its boiling point. The 
following table exhibits various thermal conditions for several ■ 
substances. 



126 



HEAT 



Critical temperature. 


Critical 
pressure 
Atmos. 


Temp. sat. va- 
por at 76 cm. 
(boil, point). 


Freezing tem- 
perature. 


Freez- 
ing 
pres- 
sure. 


Density of 

liquid. 


Water, 365° C,689°F 

Carbon dioxide, 31. 1, 88. ... . 
Air, —141, —220 


194.6 
73 

39-6 
5o 
35 
20 


IOO° C. 212° F. 

— 78.2, -108.8 

— 191. 4, —312.6 

— 182.9, —296.4 
-I95-7, -318.3 
—252.7, —422.8 


o°C.,32°F. 
-56, -69 


76 cm. 
76 


1 at 4 C. 
0.83 at o° C. 


Oxygen, —118. 8, —182 








Nitrogen, —146, —231 


-214 C, -353-2 


6 


0.885 at —194-4 











(From Kaye and Laby, Physical and Chemical Constants; and Landolt and Bernstein, Physi- 
kalisch-Chemiscke Tabellen). 

(See also Watson, Art. 232.) 

Exhibit C0 2 tubes. 

Adiabatic expansion of air from 6o° F. (521 absolute) and 
2500 pounds pressure to 14.7 pounds pressure, in doing work, 
would fall in temperature, with K = 1.408, to 11 7.5 Fahrenheit 
degrees on absolute scale or to — 342.5 F. = ( — 208.6° C). 

To liquefy a gas, it must be cooled below its critical tempera- 
ture. The gas is put under great pressure and surrounded by 
air also under such pressure and cooled to a low temperature 
by any convenient means; then the enveloping air is allowed to 
escape into the external atmosphere, and the work of its expan- 
sion against the external pressure causes its temperature to fall. 
The pipe containing the cold compressed gas is thereby cooled 
sufficiently further to liquefy its contents. This is called a 
" regenerative process." For further account of liquefaction 
processes see Watson, Art. 235. 

95. Spheroidal State. — Rapid evaporation occurs from a 
liquid in the presence of and in apparent contact with a surface 
that is at a temperature higher than the boiling point of the 
liquid; but the contact is apparent only. A drop of liquid 
placed on a hot metal plate becomes a flat globule like mercury 
on a flat surface, and moves around or trembles with a rhythmic 
motion, evaporating at a moderate rate but not boiling. Liquids 
in this condition are said to be in a spheroidal condition. Close 
examination shows that there is a very thin layer of gas between 
the liquid and the surface of the hot plate, large enough to permit a 
beam of light to be passed between the two surfaces. Phenomena 
of this kind were formerly known as "Leidenfrost phenomena." 



SPHEROIDAL STATE , 127 

To produce them, it is necessary that the surface on which 
the liquid is placed shall be considerably hotter than the boiling 
temperature of the liquid. Water thus placed on a hot metal 
plate will remain in the spheroidal condition, itself several 
degrees below boiling temperature, evaporating not very rapidly 
while the plate cools until the plate is no longer hot enough to 
maintain the condition, when the liquid comes into closer contact 
with the plate and is immediately dissipated in vapor with an 
explosive force. 

(Water may thus be evaporated on a thin metal plate which 
will finally become too cool to maintain the spheroidal condition 
and will be further cooled by the final vaporization of the water. 
But the plate may be found still hot enough to sustain a globule 
of ether in the spheroidal state. Ether may also be shown in the 
same condition on the surface of hot water.) 

The globule is actually supported on a cushion of its own vapor 
formed at a rate sufficient to hold the liquid away from the hot 
surface. The explanation of these phenomena on the kinetic 
theory is as follows: "If a surface be heated, a molecule of gas 
striking against it is heated, and leaves the hot surface with 
increased velocity. • If the surface is fixed, gas in front of it is 
driven off by bombardment of molecules which have touched the 
hot surface and, returning, strike fellow molecules; in front of the 
hot surface, therefore, the gas is under greater pressure than if 
the surface had been cold. 

If the hot surface be the front aspect of a disk, the back of 
which is by some means kept colder than the front, and if the 
disk be suspended in a gas, the heat of the front surface increases 
the pressure towards the front, and the gas flows round to the 
back of the disk. Thereafter the disk is struck on the front by 
fewer molecules with greater velocities, and on the colder surface 
by a greater number of molecules with less velocity, and there is 
compensation: the disk is equally pressed front and back and 
does not move. 

Now suppose particles recoiling from the heated surface do 
not meet other molecules, but impinge on walls of the vessel. A 



128 HEAT 

layer of particles in such condition is called a "Crookes' layer." 
This will occur in two cases: (i) when the gas is so rarefied that 
the mean free path of the molecules exceeds the distance between 
the surface and the walls of the vessel; (2) when, whatever the 
density of the gas, the opposite wall is so near the hot surface 
that the distance between them is less than the actual mean free 
path of the molecules. These conditions, which are substantially 
identical, may concur; there may be both rarefaction of the gas 
and " approximation of the opposed surfaces." The latter is the 
case with the "spheroidal state." When the distance between 
the disk and the opposite wall is very small, the vacuum need not 
be very good; the effect of the repulsion may be made manifest 
even in the open air. (Daniell's Physics, 1st ed., p. 325, q. v. 
See also Preston, Theory of Heat, Art. 54; and Barker, pp. 329 
arid 397.) 

Exhibit radiometer. 

Explanation of boiler explosions by admission of cold water 
into a superheated boiler in which water has become too low. 

May not gaseous molecules be wandering in interplanetary 
regions? 

96, Van der Waals' Equation. — According to the law of 
Charles, if the volume of a given mass of gas is constant, its 
increase of pressure is proportional to the rise of temperature; 
and, by the law of Mariotte, with constant pressure the increase 
of volume is proportional to the rise of temperature; in each case 
2 -7-3 of the volume at o° C. per centigrade degree. Then if we 
reckon temperatures from an absolute zero, pressure p and vol- 
ume v would each vary as the temperature T, or pv = RT, where 
R is a constant depending on the units for p, v and T. (See 
Art. 79.) 

From this equation it is seen that, with volume constant, 
pressure decreases with fall of temperature until, at zero, the 
pressure becomes nothing; but with constant pressure, the vol- 
ume diminishes with fall of temperature, until, at zero tempera- 
ture, the volume would be nil, — a manifest absurdity. But 
the theory upon which this proceeds takes no account of the 



CLAUSIUS' EQUATION OF THE VIRIAL 129 

size of the molecules, nor of a possible attraction or repulsion 
between them, which may vary with their distance from one 
another. That something of this latter may exist is indicated 
by the departure of gases from Boyle's law when greatly com- 
pressed; and that there is some size to the molecules is only to 
say that they occupy space. Various attempts have been made 
to formulate the relations of pressure, volume and temperature 
so as to take these conditions into account. 

Van der Waals reached the conclusion that "the effect of the 
attractions between the molecules was to add a term to p, and 

he took it to be of the form — , where a is a constant. The 

effect of the finite size of the molecules was to virtually diminish 
the volume v, in which the molecules can move, by a constant 
amount b. His modified equation then took the form 



(* + $)(? -Q- XT." 



(Watson, Art. 234, which see for fuller discussion.) 

97. Clausius' Equation of the Virial. — To provide for the 
probability that the influence of one molecule upon another is 
not negligible, Clausius called the force that may exist between 
any two molecules, F, and the distance between them s; then Fs, 
being the product of a force by a distance, is a quantity of the 
order of work or energy. Since the entire number of such prod- 
ucts would include the same product twice for each molecule, 
the effect of the interactions would be represented by ^ ZFs, 
which Clausius termed the "virial " of the molecules. 
Under the kinetic theory we had 

pv = \ MV 2 , whence \ MV* = f pv. 

The first member of this equation is the kinetic energy of the 
molecules of the gas. Clausius puts this energy equal to the 
second member plus the virial of the interaction of the mole- 
cules, or 

iMV 2 =lpv+±2Fs. 



13° HEAT 



Under ordinary conditions of such gases as hydrogen, nitrogen, 
etc., the virial is very small, but if the gas is greatly compressed 
it may naturally be expected to become relatively more signifi- 
cant. The equation may be written 



p = \ 2MV - J ZFs. 

Art. 58 showed how the value of pv first decreased with an 
increase of p and then increased, which would mean, in the appli- 
cation of Clausius' equation, that up to a certain pressure 2Fs 
is a positive quantity, or the action between the molecules is an 
attraction, but beyond that pressure (or proximity of the mole- 
cules) the quantity 2Fs is negative, or the force between the 
molecules becomes a repulsion, (pv is at first a decreasing, 
afterwards an increasing, function of p.) (See Hastings and 
Beach, General Physics, Art. 252.) 

For freezing point and boiling point of solutions, and for freez- 
ing mixtures, see Watson, Arts. 225-230. 

98. Hygrometry; Humidity. — By hygrometry is meant the 
determination of the water vapor present at any time in the 
atmosphere. 

The atmosphere is never free from moisture, and the presence 
of water vapor in a state of equilibrium means that this vapor 
exerts a definite pressure, which is a part of the entire pressure of 
the atmosphere as shown by the barometer. At a given tem- 
perature, the more moisture there is present the greater pressure 
will there be due to it, up to the point of maximum pressure of 
water vapor for that temperature. If the vapor is present in 
sufficient quantity to produce its maximum pressure, then the 
atmosphere is saturated with vapor. At that temperature no 
more vapor will exist as such; the effort to introduce more into 
a given space will result in liquefaction. Also, at the saturation 
point any lowering of temperature will result in liquefaction, 
since less vapor will produce the (smaller) maximum pressure that 
corresponds to the lower temperature. The term " humidity " 
may mean either of two things: (1) it may designate the actual 
mass of water vapor present in a given volume or given mass of 



DETERMINATION OF HUMIDITY I^T 

atmosphere, in which sense it is called the "absolute humidity ;" 
or (2) it may mean the proportion of water vapor actually pres- 
ent in the atmosphere to the quantity that would be necessary 
for saturation, i.e., the quantity present, compared with that which 
could be present. This is the sense in which the term is ordina- 
rily used, and is " relative humidity." 

99. Dew Point. — If the temperature of the air at any place 
is lowered while the surrounding air exerts a constant pressure, 
the pressure of the air and vapor whose temperature is being 
lowered remains unaltered; but as the temperature is further 
lowered it finally reaches a value for which the pressure of the 
vapor present is the maximum or saturation pressure. If the 
temperature is further lowered, not so much moisture will remain 
in the form of vapor, but some will be precipitated in liquid form. 
The temperature at which this occurs is known as the dew point ; 
the precipitation which occurs with further fall of temperature 
is dew. Dew, then, literally does "fall " upon objects from the 
atmosphere, and when the atmosphere has been cooled far below 
the dew point a good deal of moisture will be precipitated, so 
that the actual quantity of moisture remaining in the atmosphere 
.vill be less than before and the cold air will be "absolutely " 
drier than the warm was; but at the same time it will be satu- 
rated with moisture and consequently be "relatively " more 
humid, for the humidity of saturated air is 100 per cent, which 
will be the case with a small quantity of vapor when the tempera- 
ture is low and with a large quantity when the temperature is 
high. 

100. Determination of Humidity. — Various forms of instru- 
ments, or hygrometers, have been devised to determine the hu- 
midity or hygrometric state of the atmosphere. The principal 
ones are those known as dew-point instruments, and the psy- 
chrometer, or wet- and dry-bulb hygrometer. In the former 
(Fig. 53, Dines' hygrometer) the temperature of a polished sur- 
face in contact with the air is lowered until the dew appears upon 
the polished surface, and the temperature then is recorded. This 
is the dew point. The pressure of the vapor present is the same 



132 



HEAT 



as the maximum pressure of water vapor for the temperature 
of the dew point. This pressure may be taken from tables of 




Fig. 53* Dines' Hygrometer. 

maximum pressures of water vapor, which have been determined 
with great care. Also from those same tables is obtained the 
maximum pressure of vapor for the temperature of the air. 
That is the pressure the vapor would exert if the air were satu- 
rated. Now, unsaturated vapors obey Boyle's law, and the 
quantity of vapor in a given space is proportional to the pres- 
sure it exerts; therefore the quantity present, compared with that 
which could exist there, is just as the pressure 
of the vapor present is to the pressure that 
would be due to the vapor if the space were 
saturated. The ratio of these pressures, 
therefore, is the relative humidity. 
(Make determination.) 
The psychrometer (Fig. 54, wet- and dry- 
bulb hygrometer) consists of two thermom- 
eters, one of which has its bulb exposed 
directly to the air, while the bulb of the 
other is inclosed in a cloth which is kept 
moist, and from which, therefore, evapora- 
tion is constantly taking place. The effect 
of this evaporation is to lower the temper- 
Fig. 54. Wet- and Dry- a t U re of the wet bulb, and the extent to 
bulb Hygrometer. whkh the temperature shown by the wet 
bulb falls below that of the dry bulb will depend upon the rate 
at which evaporation takes place, and this in turn depends upon 
the dryness of the air. With little moisture in the air, the 




BUOYANCY OF THE AIR 133 

evaporation is rapid and the difference of the readings is con- 
siderable; with much moisture present, evaporation is slow and 
the difference of readings is small. If the air is saturated with 
moisture, no evaporation occurs and the two thermometers read 
alike. But the rate of evaporation is influenced by local con- 
ditions, such as the size of the room, or taking the observations 
indoors or outdoors or in a draft; therefore an empirical table 
or formula is necessary to reduce the indications of the instrument 
to standard values. The effort is to find the pressure of the vapor 
present in the air, and a good general formula is 

e = e' — k (ti — t 2 ) h, 

in which e is the pressure of vapor present in millimeters of mer- 
cury, e f the maximum pressure for the temperature of the wet 
bulb, ti and t 2 the temperatures of the dry bulb and wet bulb 
respectively in centigrade degrees, and h the barometer reading 
in millimeters, k is a constant, suited to the conditions under 
which the observations are made. Its value ranges from 0.00077 
to 0.0012, so that a mean value of 0.001 will give fairly accurate 
results. When the value of e is thus found, the maximum pres- 
sure / for the temperature of the air is to be taken from tables, 

and then the humidity H is the ratio of e to /, or H = - • 

(Make determination.) 

It is assumed that saturated air from around the wet bulb is contin- 
ually giving place to unsaturated from the immediate vicinity. This would 
be the case if the two bulbs were in a passage-way through which unsat- 
urated air moved from the dry to the wet bulb at such a rate as to main- 
tain the saturation as it passed beyond the wet bulb. See Fig. 55. 

Let h and t 2 be the temperatures of the dry and the wet bulb, respect- 
ively, and e and e' the pressures of vapor in unsaturated and saturated 
air. Omitting small minor corrections, suppose one gram of air to pass 
the two bulbs. Entering at atmospheric (barometer) pressure h, the 
density of the vapor compared to that of air at the same temperature and 
pressure d (= .62); then, for one gram of air, the mass of water vapor 

6 c' 

entering the passage, say at A, is -d; the mass leaving at B is — d; the mass 

h h 



134 



HEAT 



of water evaporated is the difference or -{e! - e) and if L = latent heat 

h 



of vaporization, the heat absorbed is 



Ae'-e), 



(i) 



If this is given up by one gram of air in falling from h to t, in tempera 
ture, calling sp. ht. of air 5 ( = .237), the heat so given up is 

S(k-h), (2) 

for one gram of air. Equating (1) and (2) , 




L d -(e' - e) 



S{k -it); 



whence 



— (h - k)h. 



Fig. 55. 



-Principle of the Psychro- 
meter. 



around the wet bulb. 
as 0.0007. 



For mean values, if/ 2 = 15 , d = .62 and 
£ = 587 (seep. 124), e= e' -.0006 $(h-t 2 )h 
(Draper's Heat, pp. 157, 158). In the 
sling psychrometer, the swinging of the 
instrument makes certain that the wet 
bulb is continually placed in unsaturated 
air, so that moist air is not stagnant 
For such an instrument the value of k may be taken 



1 01. Buoyancy of the Air; Reduction of Weight in Air to 
Weight in Vacuo. — The density of dry air at o" C. and 760 mm. 
pressure is 0.001293 gram per cubic centimeter, therefore a cubic 
meter weighs 1293 grams. Water vapor at the same tempera- 
ture and pressure as air is found to have a density five-eighths 
that of air. It weighs, therefore, five-eighths as much as air that 
fills the same space at given temperature and pressure. 

Example. — Suppose the barometer reading is 750 mm., the temperature 
of the room 18 and the dew point 12 , find the weight of a cubic meter of 
the air in the room. 

The vapor exerts the same pressure as that of saturated vapor at the 
temperature of the dew point, or 12 ; this is 10.46 mm., and the actual 
amount of vapor present is the amount that would saturate the air at 12 . 



ATMOSPHERIC CONDITIONS AFFECTING COMFORT 135 

The density is directly proportional to the pressure and inversely propor- 
tional to the absolute temperature. A cubic meter of air at a pressure of 
10.46 mm. and a temperature of 18 C. would weigh 

1293 X 10.46 X 273 , , 

— ^ ; — 3— ■ — -7 s2 , or 16.60 gm., 

760 X (273 + 18) 

and water vapor would weigh five-eighths as much as this, or 

16.69 X I = 10.43 gm. 
The pressure exerted by the air is 

750 - 10.46 = 739.54 mm. 
The weight of one cubic meter is 

1293 X 739-54 X 273 
760 X (273 + 18) 

This makes 1 180.51, and the total weight of one cubic meter of atmospheric 
air under the conditions named is the sum of the weights of dry air and 
water vapor, or 1190.94 gm. 

A cubic meter of dry air at the same temperature and total pressure 

T 20 7. *X 7^0 ^^ 2 7 3 

would weigh — ^— — — — . or 1197.30 gm. ; so that the presence of 

760 X 291 

moisture in the air makes it lighter. In this instance the buoyancy of the 

air upon any body in it amounts to 0.00119 gm. per cubic centimeter of 

volume. 

102. Atmospheric Conditions That Make for Comfort or 
Discomfort. — The principal atmospheric conditions that affect 
physical comfort are temperature, pressure and humidity, which 
are observed respectively by means of the thermometer, barom- 
eter and hygrometer. Cold air may be nearly saturated with 
moisture and therefore have high humidity, while containing not 
nearly so much water in it as would only partially saturate the 
air at the same pressure but at higher temperature. Place a ther- 
mometer outdoors on a cold day and it will show a low tempera- 
ture, but will probably be itself dry, but on taking it into a warm 
room it is immediately covered with moisture precipitated from 
the air, although the air of the room is said to be drier than that 
outdoors. It is drier although it contains more moisture. It is 
the relative humidity that determines the feeling of dampness. 
When the air is high in humidity and low in temperature, it feels 
raw and chilly; on the other hand, if the air is very humid and at 
the same time very warm, as in summer, the moist air carries 



136 HEAT 

away little moisture from the skin, and there is none of that relief 
from the excessive heat that is experienced when the air is dry 
enough to give the cooling effect that attends evaporation of the 
moisture from the surface of the body. It is the combination 
of heat and humidity that makes the suffocating, prostrating 
wretchedness of a hot day. In such cases, even getting into the 
shade will not bring much relief. 

Instances are on record of men entering ovens or heated 
chambers, in one instance said to be as hot as 6oo° F., and in 
some others at temperatures of 330 F. (sculptor's oven) and 
260 F. Explorers in the polar regions endure temperatures as 
low as — 70 F. 

The normal temperature of the human body being only a 
fraction over 98 F., and the boiling point of water 212 F., both 
the very high and the very low temperatures can be best endured 
if the air is dry. (2 below normal or 4 above is severe physio- 
logical derangement.) Men work in air chambers, and in sub- 
marine apparatus at depths below water of about 150 feet (as a 
limit), which corresponds to a pressure of over five atmospheres 
(about 5.4 atmospheres). The effect of rare air is more decided. 
Mountain sickness and dizziness are felt by some people at small 
elevation, even as little as 1000 feet being change enough in some 
cases to affect a weak heart; but balloonists have, in some in- 
stances, reached an elevation of five miles, where the barometer 
pressure is only about 10"; here the severity of the cold and the 
rarity of the air combine to produce severe distress to the system. 

103. Transference of Heat. — Heat is transferred from one 
point to another by the three processes of conduction, convec- 
tion and radiation. 

104. Conduction; Conductivity. — In solids, energy is com- 
municated by one molecule to its neighbor by direct impact 
without either one departing from its limited sphere of motion, 
but an increase of energy in a molecule is handed on from one 
to another until the energy is distributed throughout the body 
or communicated to another body. Such transference of heat 
through a body is conduction. The facility with which such 



CONDUCTION; CONDUCTIVITY 1 37 

transference is performed by a substance is called its conductiv- 
ity. This differs with different substances, and may be rated in 
two different ways. For instance, if two rods of different metal 
have one end thrust into a flame while the other end is kept at 
a constant lower temperature, and the temperature of the rods 
be observed at the same distances from the flame, one will be 
found to indicate a given rise of temperature at a given point 
sooner than the other will. Judged by that indication, the one 
may be said to be a better conductor of heat than the other; 
but the one that had the higher temperature might have a 
smaller specific heat (or capacity for heat), and, therefore, have 
reached a higher temperature with actually less heat than the 
other; so that the other may have actually transferred more 
heat without showing it by so great a rise of temperature. So a 
different mode of determining conductivity is preferable, namely, 
that by which the actual amount of heat transferred is consid- 
ered. This gives the absolute conductivity. If a bar of metal 
has one end in boiling water so that its temperature is constantly, 
say, ioo° C, and the other end is in contact with ice so that the 
temperature is constantly o° C, the fall of temperature along the 
bar is ioo°, and the fall per unit length, or the ratio of the total 
fall to the length, is called the temperature gradient. In such an 
arrangement as that just described the amount of heat trans- 
ferred through the bar is determined by the amount of ice melted. 
Or the number of calories is the number of grams melted X 80. 
If 61 and B 2 are the temperatures of the ends of the bar, a the 
area of cross-section, d the length of the bar, and T the time con- 
duction is going on, then it is found that for any given metal the 
total quantity of heat transferred is 

^ j_ 01 — 62 rp, 



d 

k being a constant depending on the substance that composes 
the bar. If (#i — 2 ), a, d and T are each unity, then Q = k, and 
k is the number of calories transferred and becomes the measure 
of conductivity of that substance. Thus the absolute conductivity 
of a substance is expressed by the number of calories transferred 



138 HEAT 

through a bar of the substance one centimeter long and one square 
centimeter in area of cross-section, in one second of time, when 
the two ends have a difference of one degree C. in temperature. 

If the absolute conductivity is determined for various sub- 
stances, their relative conductivities may be derived from those. 
Tables of conductivity are given in most textbooks, a few ex- 
amples being silver, 1.006; iron, 0.16; sawdust, 0.00012; horn, 
0.00009. It * s the poor conductivity of wood and organic sub- 
stances that makes wood or paper suitable for matches or 
tapers, for they can burn down nearly to the end without burn- 
ing the fingers; but paper, if very thin, will conduct heat well 
enough to make it possible to boil water in a paper cup by direct 
application of a flame, without burning the paper. 

Experiments Nos. 44, 45, 46, pages 152 and 153. Illustrating Con- 
ductivity. 

Liquids are poorer conductors of heat than are solids, and 
gases are still worse, being, in fact, almost perfect nonconductors. 

Experiment No. 47, page 153. Conductivity of Water. 
(For conductivity of gases, see Watson, Art. 241 ; and Barker, 
p. 332 to foot p. 338.) 

Examples. — 

1. If 1,150,000 calories are transmitted in an hour through an iron plate 
one centimeter in thickness and 100 sq. cm. in area when the sides are kept 
at o° C. and 20 C, what is the thermal conductivity of iron? 

Ans. 0.16 cal. per cm. per deg. per sec. 

2. When the pressure in a steam boiler is 120 lbs. gauge pressure, the 
temperature is 175 C. If the boiler is of iron 5 mm. thick, and the outside 
is at a temperature of 150° C, at what rate is heat lost through the boiler, 
for each square centimeter of surface? Ans. 8 cals. per sec. 

3. An ice house has walls 20 cm. thick, with an area of 200 square meters. 
If the conductivity of the walls is 0.00051, and the air in contact with the 
outside has a temperature of 77 F., how much ice may be expected to melt 
in a day? Ans. 1377 kg. 

105. Convection. — When a heated molecule travels from one 
place to another it carries heat, and this process is called con- 
vection. This is the commonest mode of transference of heat 
by liquids and gases, and occurs most effectively when there 



RADIATION 139 

is best circulation of the fluid. If a vessel containing water is 
heated at the top, the bottom may stay ice-cold for a long time 
while the water at the surface is boiling, but if the water at the 
bottom is heated the warm water rises through the colder and the 
liquid is gradually heated throughout by convection. The same 
applies to gases, the unequal heating of the air at different points 
of the earth giving rise to the innumerable and varied winds. 

It is by convection that heating by hot water is effected, and 
the ventilation of buildings accomplished. 

As examples of meteorological processes, if air is not saturated 
with vapor evaporation takes place at the surface of water; the 
vapor rises into the colder upper regions, where it condenses into 
clouds; these are carried by winds to distant regions, and if they 
are further cooled they are precipitated in the form of rain or 
snow, on mountains sometimes, whence they return to the sea or 
lakes to undergo a repetition of the process endlessly. 

Heavy clouds of vapor and smoke may form a covering which will confine 
ihe air beneath it. In the San Francisco fire after the earthquake there was 
no wind, no water was to be had, and a heavy pall of smoke spread above 
the city. The air rising to the height of this cover became there hotter and 
hotter, and always hotter than the regions below it, until this layer of at- 
mosphere became hottest at the top and was coolest at the bottom. Tall 
buildings remote from the flames ignited before low ones that were nearer, 
and always at the top first, e.g., the top of a steeple or the cornice of a tall 
building. Fairmont House on a hill took fire before Palace Hotel on lower 
ground although far from other burning buildings. 

Flame under a vessel is never in actual contact with the metal 
of the vessel. (Sec Barker, pp. 339 to 341.) 

106. Radiation. — The third mode of transference of heat is 
by radiation, and is displayed throughout the universe on a scale 
far transcending the other methods. 

This process implies that the energy of motion of a hot body 
is imparted directly to the universal medium, the ether, through 
which it is distributed in the form of wave motion until it is 
again communicated to gross matter through the close inter- 
dependence or connection between the ether in and around an 
ordinary body and the molecules of the body. The inter-rela- 



14° HEAT 

tion of ether and gross matter is one of the most recondite sub- 
jects of physics, but is necessarily involved in all forms of radia- 
tion through the medium of the ether. While in transit from 
one body to another the energy is that of wave motion, but when 
this is absorbed by a body it then becomes energy of molecu- 
lar motion of the body, or heat. Just to the extent that the 
body does absorb this radiant energy, to that extent is the body 
heated. No heat is evidenced by the radiation falling upon a 
body if the body does not take it up. It is then either reflected 
by the body or else it passes through the body. Heat that is 
thus reflected by a body produces no effect of heating the body, 
nor does that which passes through it. Bodies through which 
radiant heat does not pass are called athermanous, those through 
which radiant heat will pass are called diathermanous. Good 
radiators are good absorbers and bad reflectors. Good reflec- 
tors are bad radiators and bad absorbers. The absorbing and 
radiating power of a surface are equal. General law of radia- 
tion that of inverse squares. (Barker, p. 376.) 

Diathermanous bodies do not transmit heat equally from all 
sources, the readiness with which it passes through increasing 
with the temperature of the source. Thus glass transmits 
readily the heat radiated from the sun, but intercepts that from 
bodies of only a moderately high temperature, or what are called 
" black bodies." The heat from the sun will enter a greenhouse 
and heat the air and bodies within it, but the heat radiated 
from these is not transmitted but is intercepted by the glass, 
the latter being athermanous to heat from sources below 
ioo° C in temperature. The aqueous vapor in the atmosphere 
readily transmits or permits passage of the heat of the sun, 
which thus warms the earth, but the heat radiated from the 
latter is intercepted by the vapor and the clouds, and the earth 
thus cools more slowly than it otherwise would on removal of 
the sun's rays. This is noticeable in the rapid cooling of the 
earth and the air at high elevations. No dew on cloudy nights. 
For mutual relations of radiation, reflection and absorption, see 
Barker, pp. 373 to 375. 



RADIATION 



I 4 I 



In the Dewar bulb (Fig. 56 a), nitrogen, more volatile, evapo- 
rates from liquid air, and the liquid takes on a bluish hue, the 
color of liquid oxygen. Heat admitted to the interior by con- 
duction and radiation is very little; only loss is by evaporation, 
from free surface of liquid, which is slow if vessel does not receive 
heat. Rate of evaporation is from 5 to 15 per cent of what it 





Fig.- 56 (a). The Dewar 
Vacuum Bulb. 



Fig. 56 (b). The 
Thermos Bottle. 



would be from a single-walled vessel, unsilvered. Inner surface 
of outer vessel and outer surface of inner vessel are silvered. 
Evaporation of liquid oxygen surrounded by vacuum bulb, unsil- 
vered, 170 c.c. per minute. Evaporation of liquid oxygen sur- 
rounded by air chamber, unsilvered, 840 c.c. per minute. With 
a silvered vacuum bulb evaporation is less than one-half above 
rate. 

Similar conditions hold in the Thermos, Hotakold, and other 
vacuum bottles, in which none of the three processes is avail- 
able for the passage of heat to or from the material within. 

107. Prevost's Theory of Exchanges. — This theory states 
"that bodies radiate heat at all temperatures, and that the 
amount radiated depends on the body itself and not on sur- 
rounding objects; that a red-hot ball radiates the same amount 



J 42 HEAT 

of heat whether placed in the middle of a furnace or hung up in 
an ice house; that ice radiates the same amount whether in an 
ice house or hung up in front of a furnace. Bodies also receive 
heat from surrounding objects. When a body radiates more 
than it absorbs, its temperature falls ; when it absorbs more than 
it radiates, its temperature rises. If the radiation equals the 
absorption, there is thermal equilibrium, and the temperature is 
constant" (Wright, p. 90). See also, on this subject, Preston, 
Theory of Heat, Art. 229, and Barker, p. 372. 

108. Adiabatic Curves and Ratio of Specific Heats. — The 
thermodynamic condition of a body is determined by the three 
things, pressure, temperature and volume. In liquids and solids, 
a very considerable change in pressure or temperature might be 
attended by a change in volume so small as to be often negligi- 
ble; but it is not so with a gas. 

If, however, one of these three quantities is kept constant 
while the other two change, their relative values may be examined 
and plotted as a curve. 

In case the temperature remains constant, the curve showing 
the relation of pressure to volume is called an isothermal curve, 
and this has already been discussed to some extent in connection 
with gases. It is to be noted, however, that with a decrease of 
volume in a given mass of gas the temperature will rise unless 
some means is provided to carry off heat, and, vice versa, if the 
gas expands (against pressure) its temperature will fall unless 
at the same time heat is communicated to it from some other 
body. If, then, the gas could be so confined in a nonconducting 
chamber that no heat could be admitted to it or could escape 
from it, such a vessel would be adiabatic, the changes in the con- 
dition of the gas with varying pressures and volumes would be 
adiabatic changes, and the curve showing the relative values of 
p and v would be called an adiabatic curve. 

In the isothermal, this relation is expressed by the simple 
equation pv = const, and the curve is an equilateral hyperbola. 

In the adiabatic, it may be shown by a somewhat difficult 
demonstration that the relation is given by the equation 



LAWS "OF THERMODYNAMICS 143 

p<D k = const., in which k is the ratio of the specific heat of the 

C 

gas at constant pressure to that at constant volume, or k = — -. 

(See Watson, Art. 259.) 

A gas that is compressed or rarefied without change in the 
quantity of heat, i.e., adiabatically, would undergo change of 
temperature, and of course would not conform to Boyle's law; 
neither would the relation of the change of pressure to the change 
in volume be the same as if the temperature were constant, but 
it can be shown that this ratio would be k times as great in an 
adiabatic change as in an isothermal change. (See Watson, 
Art. 259, and Hastings and Beach, Art. 241, "The Two Elasticities 

stress 

of a Gas.) This ratio, is, however, — , which is the measure 

'strain' 

of the elasticity. The elasticity, then, of a gas that is com- 
pressed or rarefied adiabatically is k times as great as if the 
gas could lose or gain heat at such a rate, while being compressed 
or expanded, as to keep its temperature constant. In the latter 
case we have seen (Art. 59) that the elasticity of a gas is numeri- 
cally equal to the pressure; in an adiabatic change the elasticity 
equals k times the pressure. (See infra, Art. 125, "Velocity of 
Sound in a Gas.") 

109. Laws of Thermodynamics; Dynamical Equivalent of 
Heat. — The fundamental relations of heat and mechanical 
energy are embodied in two principles, known respectively as 
the First and the Second Law of Thermodynamics. 

The first law is that any definite amount of mechanical work is 
convertible into a definite quantity of heat, and, conversely, any given 
quantity of heat is capable of performing a definite amount of work. 
The exact ratio of the amount of work to the quantity of heat it 
can produce is called the mechanical (or dynamical) equivalent 
of heat. It is the number of work units that correspond to one 
heat unit. This number will obviously depend upon the units 
in which both work and heat are measured. It might be the 
number of foot-pounds necessary to produce one British thermal 
unit (which would be 778), or it might be the number of gram- 
meters that would produce one calorie (which would be 427), or 



144 HEAT 

in absolute c.g.s. units it is the number of ergs that produce one 
calorie (4.184 X io 7 ergs). 

The estabHshing of this law was the beginning of modern 
physics as a science of energy. It was the culmination of work 
that may be said to have begun when Count Rumford showed 
that heat could not be material, and so displaced the earlier 
" caloric " theory of heat. The theoretical principles of heat as 
a form of energy were developed by a number of philosophers, 
prominent among them being Rankine, Clausius, Julius Robert 
Mayer and others, but the experimental investigations estabHsh- 
ing the exactness of relationship between heat and work are due 
chiefly to James Prescott Joule of Manchester, England. An 
account of the labors of Mayer is given in the last lecture in 
Professor Tyndall's Heat a Mode of Motion, and the work of 
Dr. Joule is published in full in two large volumes. The account 
of this work forms one of the most interesting and most impor- 
tant chapters in the history of physical science. 

Dr. Joule determined the mechanical equivalent of heat by a 
series of experiments that are now classical, but, besides the direct 
determinations, he made indirect ones by means of heat produced 
electrically and also chemically, and thus showed not only the 
connection between heat and mechanical energy, but also the 
interrelation of both of these forms with chemical action and 
electric currents. This was the first unfolding of the physics of 
to-day, and dates from about 1850. (Vide infra, Art. 198.) 

Many redeterminations by various methods have been made 
since Dr. Joule's reports, the best being summarized in Watson, 
Art. 251, and in Hastings and Beach, Arts. 226 and 227. 

The second law of thermodynamics embodies certain principles 
that are by no means so simple as the one constituting the first law, 
although the second law has been cast in two or three forms that 
sound simple enough. Clausius puts it: "It is impossible for a 
self-acting machine, unaided by any external agency, to convey heat 
from one body to another at a higher temperature" This is so 
paraphrased as to say that heat cannot of itself pass from a cold 
body to a hot body, and if by any means we cause heat to be 



SOURCES OF HEAT 145 

transferred from a body to another at a higher temperature, we 
must in the process supply the system with energy from some 
outside source. So Lord Kelvin states the law: " It is impossible, 
by means of inanimate material agency, to derive mechanical 
effect from any portion of matter by cooling it below the tempera- 
ture of the coldest of surrounding bodies." (See, on this subject, 
both Watson, and Hastings and Beach.) 

This law has been the subject of much discussion, but its- 
bearings are chiefly in abstruse relations of thermodynamics or 
else in the possibilities of heat engines, and therefore will not 
be further considered in this course. 

Examples. — Take 1 calorie = 427 gram-meters, or 4.19 X io 7 ergs. 

1. What is the heat value of 10,000,000 ergs? Ans. 0.2387 cals. 

2. If the water at Niagara Falls drops 50 meters, how much is its tem- 
perature raised by its stopping? Ans. o.ii7°C. 

3. A weight of 100 kg. in descending 20 meters rotated a stirrer in a 
calorimeter containing 984 g. of water, and the temperature was raised 
4.7 C. If the water equivalent of the calorimeter was 16 g., what does 
this give for the mechanical equivalent of heat? 

Ans. 425.5 gm.-meters/cal. 

4. If one-half of the heat from the impact of a leaden bullet against a 
wall at 16 C. is taken up by the lead, what must be the velocity of the 
bullet that it may be melted? (Take sp. ht. of lead, 0.032, melting point 
326 C, and latent heat of fusion 5.36 calories per gram.) 

Ans. 506.5 meters per second. 

5. The combustion of 1 gram of coal liberates 8000 heat units (calo- 
ries). If 2,000,000 liters of water are to be pumped from a well in which 
the surface of the water is 30 meters below the level to which it is to be 
raised, how much coal must be burned, supposing the engine can apply 
1 5 per cent of the heat to useful work in raising the water? Ans. 117 kg. 

6. From the value in ergs of the gas-constant R, given in Art. 79, show 
that it is almost exactly 2 calories. 

no. Sources of Heat. — We recognize heat as resulting from 
various processes, every one of which is a transformation of 
energy from some other form into this form, as : 

Chemical action, of which the most common instance is com- 
bustion; but there are many other chemical combinations in 
winch energy is liberated in the form of heat; this energy is then 



146 HEAT 

said to be energy of chemical separation possessed by the bodies 
before their combination. 

Mechanical action, whenever it increases the molecular motion 
within a body. It may be stirring, hammering, twisting, bend- 
ing; or the increased molecular motion may be brought about by: 

(a) Friction; 

(b) The compression of gases ; 

(c) The passage of an electric current; 

(d) Direct radiation from the sun. 

(Illustrate with fire syringe; incandescent electric lamp im- 
mersed in water; sun glass. For chemical action see Barker, 

PP-352-357-) 

Most of the effects of chemical action (certainly all of combus- 
tion), and most of mechanical action (other than efforts of 
animals), can be traced ultimately to the sun; for the vegetation 
which supplies fuel, whether the coal formed in past ages or the 
wood of to-day, is due to sunlight; and hence also is all our steam 
power. The power of winds and of waterfalls is also, as we have 
seen, directly attributable to the ceaseless action of solar radia- 
tion, and our sources and our supplies of energy other than these 
are inconsiderable. 

in. Solar Constant. — But, apart from the chemical effect of 
sunlight, the heat emitted by the sun as such, and the quantity 
received from the sun by the earth, is measurable, and when ex- 
pressed quantitatively, the latter is called the solar constant of 
radiation. The latest determinations of this quantity make it 
very nearly 2 calories per square centimeter per minute on a nor- 
mally exposed surface above the atmosphere, which is reduced 
about one- third at sea level by atmospheric absorption; or, on the 
surface of the sun, enough heat is radiated to burn 1400 pounds 
of coal per hour on every square foot of the sun's surface. 

To account for the maintenance of such a supply of energy 
thus dissipated into space is a problem that has long taxed 
physicists and has called forth numerous hypotheses. (See, on 
this subject, Barker, pp. 357-361, and The New Knowledge by 
Robert Kennedy Duncan.) 



EXPERIMENTS TO ILLUSTRATE CHAPTER II. 



Experiment No. 32, 
and Contraction. 



Art. j 2. Nos. 32 to 35, incl., illustrate Expansion 



Gravesande's ring (Fig. 57) is a flat ring of brass that passes easily but 
closely over a hollow sphere of copper. On heating the ball with the flame 
of a lamp or Bunsen burner, if the ring is brought up from below the ball, 

the latter is too large to pass through the ring 
and is raised up. As the ball cools and the 
ring is warmed, the contraction of the former 
and the expansion of the latter presently per- 
mit the ball to drop through. The experiment 
holds good with the ball in any position, show- 
ing expansion in all directions. 

Experiment No. 33, Art. 72. Compound 

Expansion Bar. 
A strip of iron about 60 cm. long, 15 or 18 
mm. wide and 2 mm. thick is riveted at inter- 
vals of about 5 cm. to a brass strip of the same 
size. 

At a certain temperature this compound bar 
is straight and will lie flat on the table. If 
it is heated, however, preferably by several 
burners at different points, the two metals in 
contact undergo the same rise of tempera- 
ture, but the bar acquires a considerable curvature, and will turn like 
a rocker on the table. The brass being more expansible is on the outer or 
long side of the bow, but if the bar had been much lowered in temperature, 
say, by immersing it in a freezing mixture, the curvature would have been 
in the opposite sense; the brass would be shorter than the iron and con- 
sequently would be on the inner side of the arc. 

Experiment No. 34, Art. 72. 

Trevelyan's rocker (Fig. 58) is a prism and bar of brass or copper that 
rocks easily on the edges of a groove along one side of the prism. The prism 
is heated nearly to the melting temperature of lead, and then laid across 
the edge of a triangular prism of that metal, the latter, as also the end of 
the bar, resting on the table. On giving a slight rocking movement to the 

147 




Fig- 57- 



148 HEAT 

brass prism, the rocking is maintained by the sudden jutting up of micro- 
scopically minute nodules of lead against the edge of the groove that is for 




Fig. 58. 

the instant in contact with the lead, and the instrument sings a clear but 
varying note. 

(The secret of success is to have the edges of the groove and also the 
contact edge of the lead clean and bright. The lead prism should lie firmly 
on the table.) 

Experiment No. 35, Art. 72. 

The contraction of rubber on being heated may be shown as follows: 
A piece of soft (black) rubber tubing T (Fig. 59), about 2 ft. in length 

and a quarter-inch bore, is fitted at 

each end over a short pipe (prefer- 
ably brass) , to which it is secured by 

wrapping it with cord. The upper 

end is clamped, or suspended from a 

hook at the height of 4 or 5 ft. above 

the table or floor. From the lower 

end suspend a weight of 3 or 4 lbs. to 

stretch the tube T until the weight 

lightly rests upon the table or floor. 

By a string 5 connect the lower end 

of T with the short arm of a pointer 

P, and adjust the length of the string 

so as to set the index end of the 

pointer at the zero of a scale. Arrange 

a boiler as in the figure, near the upper 

end of the rubber tube. A connecting 

tube b will permit steam to pass from 

the bent tube a of the boiler to the 

rubber tube T. 

When steam is issuing freely from 

a of the boiler, connect b with a and 

close c. The steam passing through 

the rubber tube T causes it to contract, raising W probably 3 or 4 cm. 

The contraction is more plainly seen in the movement of the pointer over 

the scale. 




Fig. 59. Rubber Contracts 
when Heated. 



EXPERIMENTS 



149 




Fig. 60. Capacity for Heat. 



When the tube has been stretched in the first place by the weight W, the 
latter should rest on the table lightly just when the steam is admitted at b; 
otherwise the tube continues to be drawn out for some time by the weight. 

Experiment No. 36, Art. 82. Differences in Thermal Capacity. 

Balls of copper, iron, zinc, tin and lead of equal mass will not differ 
greatly in diameter, except the lead, which will be much smaller than the 

others. These balls in a bath 
of boiling water will acquire a 
common temperature of about 
ioo° C. 

At this temperature place 
them upon a cake of beeswax 
about 4 mm. in thickness. 
They will all begin to melt the 
wax and they will cool off by 
loss of the heat of fusion of the 
wax, but they will continue the 
melting so long as their temper- 
ature is above 62 C, i.e., while their temperature falls through 38 degrees. 
If they all had the same capacity for heat, they would all give out the 
same amount of heat in changing through this common range of tempera- 
ture, and consequently all would melt the same amount of wax. It is seen, 
however, that the iron ball will melt its way through (and possibly a second 
time), the copper will melt through and partly again, the zinc will probably 
about melt through, the tin scarcely halfway, while the lead, which would re- 
quire a smaller orifice than any of the others, will make very little impression. 
Observe, it is not at all a question of which one melts the wax the fastest, 
but the most, i.e., which has the most heat to supply in a given change of 
temperature. The one which has the least 
might be a better conductor than another 
and so part with its heat more rapidly. 

Instead of beeswax, a somewhat thicker 
cake of paraffin may be used. Its melt- 
ing temperature is 53 ° C. 

Experiment No. 37, Art. 88. Regelation. 

The wire (Fig. 61) passes through the 
ice by the process described in Art. 88, 
but it is always solidly incased in ice; 
the latter is not cut apart. Air which is Fig. 61. Freezing Point of Ice 
in separate large bubbles in the block is is Lowered by Pressure. 




IS© 



HEAT 




Fig. 62. 

Vapor Pressure 

Tubes. 



now seen along the plane of section in minute bubbles, giving a gray 
appearance like that of ground glass. 

Experiment No. 38, Art. 89. Nos. 38 and 39 show Vapor Pressures. 

If several barometer tubes (Fig. 62) are filled with mer- 
cury and inverted over a reservoir of that liquid, the column 
in each tube will stand at a height, under normal atmos- 
pheric pressure, of 76 cm. If, now, a drop or two of 
water be introduced into a tube as in the figure, the 
water rises to the top and in the vacuum it instantly 
changes into vapor. The pressure of this vapor forces 
the column of mercury down, against the external atmos- 
pheric pressure. Introducing other liquids into the other 
tubes, each vapor will be found to exert a pressure peculiar 
to itself. Thus, if the temperature is 20 C, water vapor 
will force the top of the column from 76 cm. down to 
74.26 cm., exerting a pressure of 1.74 cm.; alcohol to 
71.55, showing a pressure of 4.45 cm.; and ether will force 
it down to 32.67, with a pressure of 43.33 cm. Use tubes of at least 4 mm. 
bore and use different pipettes for inserting the different liquids. 

Experiment No. 39, Art. 89. 

On a tube T (Fig. 63) blow a thin bulb B, about 2 cm. in diameter. Fill 
the bulb half full of water (most simply done by allowing it to draw water 
in as the bulb cools), and draw the end of the 
tube to a capillary C. A bottle F of about 
200 c.c. capacity and rather thick glass has a 
rubber stopper with two holes. Through one 
orifice passes T, through the other a manometer 
tube containing oil. When the stopper is in 
place, the manometer tube is raised or lowered 
through A until the pressure in the bottle is 
equal to that of the atmosphere, which is shown 
by the oil being at the same level in both 
branches. The air in the bottle should be dry. 
The capillary end C is now sealed by the flame 
of a Bunsen burner or a blowpipe. By manipu- 
lating the tube T the bulb B can be pressed or 
rubbed against the side of the bottle and be 
broken and the water liberated. The vapor saturates the space in the 
bottle and the vapor pressure is at once shown by the movement of the oil 
in the bent tube. 









C 




T 


/ 


Hv 






__]- 




\ 


%£ 


r 


\ 




B 



Fig. 63. 



Vapor Pressure 
Bottle. 



EXPERIMENTS 



151 



Experiment No. 40, Art. gi. 

(a) Culinary Paradox; to make water boil by cooling it. 

Boil water in a flask of thin glass (Fig. 64), stop neck of flask securely, 
invert flask, and soon ebullition ceases, as the temperature falls. The ap- 
plication of cold water to the part of the flask inclosing the vapor condenses 
the latter, lowers its pressure, and the water again boils violently. 





Fig. 64. The Culinary 
Paradox. 



Fig. 65. Boiling is Renewed under 
Reduced Pressure. 



Experiment No. 41, Art. gi. 

(b) Experiment No. 40 is well modified as follows. (Carhart's Uni- 
versity Physics, Part II, Art. 45.) 

Arrange apparatus as in Fig. 65; have flask stopped tightly, and boil the 
water until steam issues freely from the tube. Remove the burner, and 
when the water is no longer boiling, raise the vessel A containing cold 
water, until the tube dips well down in it. As the vapor in the flask cools, 
its pressure decreases ; water rises through the tube, and, entering the flask, 
greatly reduces the vapor pressure, and violent ebullition ensues. 

Experiment No. 42, Arts, gi and g2. 

Freezing water by its own evaporation, or by the evaporation of a liquid 
surrounding it (a), by the cryophorus (Fig. 66). 

Have the upper bulb of the cryophorus less than half full of water to 
prevent breaking of the glass when the water freezes. Pack the lower bulb 
in a freezing mixture of coarse salt and crushed ice, about one volume of 
salt to two of ice. Condensation of vapor in the lower bulb reduces the 
pressure upon the liquid above and evaporation goes on rapidly though 
quietly in the upper bulb, absorbing heat from the liquid there, and if this 



152 



HEAT 



absorption of heat is more rapid than the communicating of heat from the 
air of the room, the temperature falls and the liquid freezes, — usually in 
twenty minutes to a half hour. 





Fig. 66. The 
Cryophorus. 



Fig. 67. Freezing Water by 
Evaporation of Ether. 



Experiment No. 43, Arts, gi and Q2. 
In a large test tube (Fig 67), containing sulphuric ether, place a small 
stopped tube containing one or two c.c. of water. Agitate the ether by 
blowing through a tube O; it rapidly evaporates and cools the water to 
freezing. A thermometer in the larger tube shows the progress of the fall 
in temperature. 

Experiment No. 44, Art. 104. Heat Conduction. 
Place a wire gauze containing 50 or more meshes to the inch about an 
inch above the top of a Bunsen burner, turn on the gas and ignite it above 
the wire gauze. The gas burns above the metal but does not extend below 
it, the metal conducting away the heat fast enough to prevent the under 
surface from getting hot enough to ignite the gas. 

Experiment No. 45, Art. 104. Nos. 45 and 46 illustrate Differences in 

Conductivity. 

From a massive ring of brass (Fig. 68), radiate rods 
of various metals about 5 cm. long and 4 mm. thick. On 
the ends of these are placed small pieces of phosphorus, 
and the central ring is heated by a gas flame. The 
phosphorus ignites when the end of the rod rises to the 
necessary temperature, and the difference in conductivity 
of the rods is seen in the longer time required by one than 
by another to produce ignition. Fig. 68. 




EXPERIMENTS 



153 



Experiment No. 46, Art. 104. 
If a wooden cylinder (Fig. 69) be fitted into the end of a brass tube of the 
same external diameter, and a single thickness of paper be made to en- 




Fig. 69. 

circle snugly both the brass and the wood, the flame of the burner at the 
junction will char the paper around the wood, but not that inclosing the 
brass which rapidly conducts the heat away. 



Experiment No. 47, Art. 104. Poor Conductivity 
of Water 
An air bulb of about 5 cm. diameter (Fig. 70), 
has its stem dipping into a liquid (colored water), 
and is covered with water to a depth of about 
3 mm. above the bulb. The index liquid stands 
about halfway up the tube. The air in the bulb 
is sensitive to very small changes of temperature; 
the warmth of the fingers placed upon the bulb 
at once moves the liquid down the tube. Pour 
a very thin layer of ether on the water over the 
bulb and ignite it. The flame spreads over the 
surface of the water, but no heat is conducted to 
the bulb, though the heat is intense and the depth 
of liquid very small. When, finally, the index 
does show a warming of the bulb, it is an effect 
of radiation rather than of conduction. 




Fig. 70. 



CHAPTER III. 
WAVES AND WAVE MOTION. 

(Preliminary to Sound, Light and Electricity.) 

112. Introduction and Use of Wave Theories. — Probably 
the earliest appreciation of waves was derived from the disturb- 
ance in the surface of a body of water, and this would be im- 
mediately extended to liquids generally. Waves in gases could 
hardly have been recognized until much later, and waves in solids 
must have been unthinkable without a considerable development 
of the science of elasticity. However, elasticity, as a property 
of bodies, must have been known early, perhaps before inertia 
itself, since early ideas were to the effect that a body in motion 
would " naturally" come to rest of itself — an erroneous con- 
ception in regard to inertia. 

The idea of waves in physics has become so extended and 
generalized as to lead to this statement: " A wave is a progressive 
form due to the periodic vibration of the particles of the medium 
through which it moves To prove that any phenom- 
enon is due to wave motion it is sufficient to show, first, that it 
is periodic; second, that it is propagated with finite velocity." 
(Hastings and Beach, pp. 514, 606.) 

An examination of this broad statement will at once show that 
wave motion attends a wide range of physical phenomena, con- 
nected possibly with every medium in the universe, or wherever 
an effect is produced in a body on one side of a medium by an 
agent on the other side of it, for so far as known, all such dis- 
turbances require time for their transmission, and many of them 
are periodic in character. 

113. Vibratory Motion and Wave Forms. — If motion of a 
body or particle is vibratory, that at once means periodicity; 
but periodicity does not necessarily mean motion to and fro in a 

154 



VIBRATORY MOTION AND WAVE FORMS 1 55 

straight line. It is a recurrence to a given position at regular 
intervals and a successive repetition of its movement through 
various positions in the same order. It will always give the 
effect of a to-and-f ro movement in a straight line if the component 
of its motion in a given plane could be viewed from a point in 
that plane. For example, if a body moved in a circle, Fig. 71, 




B 

Fig. 71. Vibration in Simple Harmonic Motion. 

describing successive revolutions in equal periods of time, from 
A through C, B, and on again through A, this motion would be 
periodic, and, to an eye in the plane of the circle and far distant, 
the body would vibrate across a diameter. If the circle itself 
were at the same time turning about an axis, as AB, then, to an 
eye on the fixed line OX, the body might describe a complex 
figure, but its movement would be periodic, and at any instant 
could be resolved into two straight-line vibratory motions along 
two diameters of the circle. 

If we start with the uniform motion of a particle around a 
circle, as above, its motion is a combination of two S.H.M.'s along 
two diameters. The amplitude of vibration is the extent of the 
departure from its mid-position, in this case the radius of the cir- 
cle; and the period is the time that elapses between the passage 
of the particle through a given position and its next passage 
through the same position in the same direction. 

If, now, we consider the motion of this particle to be communi- 
cated to neighboring particles in the same medium, and we follow 
the effect in one direction, say, to the right of the figure, let us 
suppose a certain time to be required by each particle in succes- 
sion to acquire the motion from its predecessor and transmit it 



156 WAVES AND WAVE MOTION 

to its successor; then a chain of particles will have been set in 
similar motion by the time one particle, as A , will have described 
one revolution; i.e., in one period T. The length of this chain 
is the distance the disturbance travels in one period, and is a 
wave length, X. The particle next following the last in this 




Fig. 72. Lyman's Apparatus illustrating Waves in Liquids. 

chain is starting upon its motion as A is beginning its second 
period. The motion of any one particle may be regarded as 
vibratory, but the wave comprises all the particles set in vibra- 
tion in one period. If these particles are in a liquid with a free 
surface, the effect is to put the surface into the form usually 
recognized as a wave. (Shown by the circular motion of parti- 
cles in a line, as in Fig. 225, Watson, p. 343, and also on the 
Lyman's wave apparatus, and in the water waves on the Colum- 
bia wave machine.) 

If, in Fig. 71, the amplitude of vibration along CD diminishes 
while that along AB remains the same, the circle becomes an 
ellipse with its longer axis vertical, and if we consider this change 
carried to an extreme we get simply a motion up and down on 
the line AB. This motion, communicated to the particles in one 
direction, say, as before, to the right, will be taken up and trans- 
mitted by the particles successively, and the wave form will be 
the sine curve of equal crests and troughs, eVery particle de- 
scribing S.H.M. across the line of propagation of the disturbance. 
The wave in this case is said to be due to transverse vibration, and 




VIBRATORY MOTION AND WAVE FORMS 157 

is sometimes called a 
transverse wave. It is 
shown in the upper part 
of Fig. 73. 
But if, in the same 

Fig. 73- Wave Forms due to Transverse and ^ we conskkr the 

to Longitudinal Vibration. 

amplitude in the vertical 
direction to be diminished, while that in the horizontal direc- 
tion is unchanged, it would result ultimately in a to-and-fro 
motion along the horizontal diameter, and the effect upon the 
particles along a horizontal line in the direction of motion, say, to 
the right, would be a crowding together, followed by a with- 
drawing or separating of the particles ; a crowding so long as the 
initial particle was moving from left to right (or during half of 
a period) , and a separating so long as it was moving from right 
to left (or during half of a period). One half of the wave, then, 
would be in a state of condensation, and one half in a state of 
rarefaction, every particle describing S.H.M. along the line of 
propagation of the disturbance. The wave in this case is said 
to be due to longitudinal vibration and is called, sometimes, a 
compressural wave, — more commonly a wave of condensation 
and rarefaction. This is shown in the lower portion of Fig. 73. 

Experiment No. 48, page 168. — The waves resulting from these three 
modes of movement are all exhibited on the Columbia wave apparatus. 

While we may thus examine the vibration of any single 
particle, and, if complex, resolve it into its simple elements, the 
wave form is the outline of the positions occupied at any instant 
by all the successive particles in one line that have been set in 
motion successively during the time that the initial vibrating 
particle has required to complete its motion, and return to its 
first position to start upon a repetition of its motion. A simple 
vibratory motion back and forward continually in the same line 
can be traced along any line as a succession of simple waves, but 
a complex vibration will give a complicated form that can be 
resolved into simple ones of various periods and amplitudes. 



i58 



WAVES AND WAVE MOTION 



For example, if the particle at O, Fig. 74 a, should describe a 
figure 8 in the rectangle by following the direction of the arrows, 
it will complete its vibration by crossing the rectangle 
four times horizontally and twice vertically. The 
wave movement along a line of particles would be 
twisted and difficult to show in a diagram, but it 
could be resolved into motion in the vertical and the 
horizontal planes separately, as shown in Fig. 74 b, 
in the length of one wave of that component of the motion which 
has the longest period; i.e., the one with the vertical movement. 




Fig. 74 a. 




V V 

Fig. 74 b. Wave Motion in Two Planes. 

It has been shown by Fourier (Theorie Analytique de la Cha- 
leur) that any complex periodic curve which consists of an exact 
simple number of vibrations will present along a line of particles 
a complex wave form that can be analyzed as a series of simul- 
taneous component wave forms of simple character. 

114. Wave Front. — When a vibrating particle communicates 
its motion to the next one, and that to another, and so on along 
a given line, the resulting wave may be traced along that line, 
but this "next one " receives the motion only because it is 
"next," and there is such an one in all directions around the one 
first considered. A wave motion then is started and proceeds 
throughout a medium in all directions, and if the disturbance 
travels at the same rate in all directions, the boundary of dis- 
turbance at any instant will be the surface of a sphere about the 
initial point of disturbance as a center. In the case of waves at 
the surface of a liquid the boundary becomes a circle. This 
boundary is called the wave front. 




VELOCITY OF PROPAGATION 1 59 

As the disturbances advance there is at any instant a line or 
surface of disturbed particles, and each of these particles is 
regarded as itself the source of a disturbance that is to be propa- 
gated further. The complete investigation of such propagation 

through a medium is exceedingly 
abstruse, but it can be shown that 
the effect is to produce little or no 
disturbance at a given instant 
except in the wave front. Thus 
a disturbance proceeding from a 
single point, as 0, Fig. 75, will 
presently have advanced to ABC. 
If each point of this line ABC be 
taken as a center and circles be 

Fig. 75. Huyghens' Construction , ., ■. .,, , v« .li 

of Wave Front described with equal radii, then 

in the time needed for the disturb- 
ance to travel the length of such radius, it will lie chiefly in 
the tangential boundary DEF, which again is a sphere or circle 
with as its center. 

If ABC were a straight line in the surface, as of water, DEF 
would be a parallel straight line; and if ABC represented a plane 
surface, DEF would also be a plane wave front, parallel to ABC, 
and might be regarded as proceeding from a point O at an 
infinite distance. 

115. Velocity of Propagation. — The conventional form chosen 
to represent a wave is the same whether the wave results from 
transverse or longitudinal vibration, or from circular motion, 
and consists of alternate crests and troughs. 

In the case of transverse vibrations this form properly corre- 
sponds to the actual position of successive particles in the line 
of propagation. In the case of longitudinal vibration, where the 
particles are alternately crowded together and separated, the 
ordinates of this sine curve must be understood as corresponding 
to the displacement of the successive particles from their normal 
position, but laid off in a transverse direction. The curve does 
not directly represent the shape of the wave. 



i6o 



WAVES AND WAVE MOTION 



In all cases the wave length X is the distance the disturbance 
advances through the medium in the time of one vibration. It 
is the distance from any particle to the next particle that has 
the same displacement and is moving in the same direction. It 
is the distance from crest to crest or from trough to trough; 
from condensation to condensation or from rarefaction to rare- 
faction ; from crest to trough or from condensation to rarefaction 
is half a wave length, § X. 

If T is the period, i.e., the number of seconds for one vibration, 

i 



then in one second there will be — vibrations. 



Calling the num- 
ber per second n, this is the frequency or the vibration rate. If 
n waves per second follow upon one another, each of a length X, 
the disturbance in one second along a line of particles will be a 
train of n waves, and the distance the disturbance will have 
traveled is n\\ or the velocity of propagation is v = n\; from 
which relation if either two quantities are known the third may 

be determined. Also, if for n we put its value — we have v = —• 

116. Reflection of Waves. — Suppose a wave front, for sim- 
plicity, say, a plane wave front, as it advances through a given 
medium, encounters the surface of a medium of different density. 
If, for example, this be a wall, the advancing waves will be 
reflected. If the ad- 
vancing wave front 
is at an oblique angle, 
the reflected waves 
will proceed in such 
a direction that the 
reflected wave front 
makes an angle with 
the reflecting surface 
equal to that made 
by the incident wave front (measured the other way). In Fig. 
76, if the full lines represent advancing wave fronts, the broken 
lines will represent the reflected ones after the encounter with 
the surface AB, and it is seen that for even such a limited wave 




Fig. 76. 



c E 

Reflection of Plane Wave Front. 



REFLECTION OF WAVES l6l 

front, there is a portion of the medium CDE which will be dis- 
turbed by both systems of waves, the incident and the reflected. 
If AB were the surface of an elastic medium, part of the energy 
of the advancing waves would go to setting up vibrations in this 
medium, and waves would continue to advance in it, the reflected 
waves possessing less energy than if AB were unyielding. 

If we consider a single line of waves instead of a wave front, 
and the reflecting surface is normal to the line of waves, the 
reflected waves will retrace the same line of particles along which 
other waves are advancing. The result of this will be that if a 
particle in the advancing waves is met by the returning wave so 
that the particle would be impelled to move in the opposite di- 
rection (say, the advancing one moving upward and the reflected 




D 
Fig. 77. Stationary Waves. 

one downward) ,' then if the amplitude of vibration were alike 
for each system, that particle would be undisturbed, as at B, 
Fig. 77, but a quarter of a wave length further along from the 
reflecting surface, the advancing one would not be so far up (it 
would be in its lowest position), and the reflected one would be 
farther down (it would be in its lowest position), and the de- 
pression would be doubled in extent as at D; a quarter of a wave 
length nearer the origin of motion the particle in the advancing 
wave would be on the axis line but going down and that in the 
reflected wave in the same position but going up, and again the 
particle would be stationary as at C. At that particular instant 
the line of particles would have the position of the full line AC BO; 
a half period later they would have the position of the dotted line 
AC BO, the particles at A, C, B, and O remaining stationary. 
These points are called nodes, the broad places or those of greatest 
disturbance being loops or ventral segments. Such waves are 
called stationary waves. 



1 62 WAVES AND WAVE MOTION 

A similar effect is produced if the waves are due to longitudinal 
vibration, the nodes being due to motion imposed upon a particle 
in opposite directions at the same time, and corresponding, there- 
fore, to condensation or rarefaction but minimum movement, 
while the loops correspond to freest movement in either direction 
along the line of propagation. The nodes, as in the former case, 
are half a wave length apart, are places of rest, and are alter- 
nately condensed and rarefied conditions, while the loops are 
places of largest movement alternately in the direction of the 
advancing and the reflected waves. From node to node or from 
loop to loop is half a wave length. From node to loop is one 
quarter-wave-length. 

Experiment No. 4g, page 168. — Stationary waves with spiral rope. 

117. Interference. — A train of reflected waves is like an in- 
dependent set of waves proceeding from a different source from 
that of the incident waves. When such waves retrace the same 
line as the incident ones traverse, the effect is the same as if the 
line had been traversed by waves from two different sources. 
When waves proceed from two sources it may happen that at 
places in the medium where there would be the crest of a wave 
from one source there would be a trough from the other. At this 
place the waves are said to "interfere" and neutralize each other. 
In the case of stationary waves there is interference at the nodes. 
Midway between the nodes the effect of either wave is height- 
ened by the other, constituting what is termed "reinforce- 
ment." 

If waves proceeding from two independent sources and spread- 
ing throughout a medium, are alike in period, they will produce 
interference continually at the same places, so that these quies- 
cent places may be traced out as "interference bands." If the 
periods are not alike or commensurate in some simple ratio, the 
positions of interference are shifting and may be difficult to 
recognize. 

Waves proceeding from one point may be brought to a focus 
elsewhere by reflection from a curved surface. Thus if they 



PHASE OF REFLECTED WAVES 1 63 

proceed from one focus of an ellipse they will converge upon the 
other focus. A train will thus be sent out from each focus and 
they will produce interference bands. (See Watson, Fig. 229.) 

Experiment No. 50, page 168. — Interference of waves in surface of mer- 
cury, projected by reflection. 

118. Phase of Reflected Waves. — We confine our attention 
to waves that meet a reflecting surface perpendicularly, and 
are therefore reflected directly upon themselves. In the case of 
water waves, an examination of the movement of particles so as 
to form the wave will show that if the reflecting surface is met 
by the crest of the advancing wave this will be reflected also as 
a crest, and the reflected wave is said to be in the same phase as 
the incident. But if the waves are due to the elasticity of the 
medium and are advancing along any line OD, which is fixed at 
D, this point is of necessity a node, and whatever the phase in 
which the advancing wave arrives at D, the returning wave must 
have at D such a phase of vibration as to neutralize vibration 
there. For this, the reflected wave must be reversed in phase, 
and must retrace the line DO as if it had undergone a retarda- 
tion of a half wave length. 

When a transverse vibration travels from a rarer to or into a 
denser medium, that part of the vibration that is reflected, and 
therefore returning through the rarer medium, is reversed in 
phase, or moves as if retarded a half period; but in proceeding 
from a denser into a rarer medium, no such reversal occurs. 

When a longitudinal vibration travels from one medium into 
another, the circumstances of reversal of phase are just con- 
trary to the above. (See Watson, Arts. 277, 300; and Hastings 
and Beach, Art. 471; see also infra, Art. 243, Newton's 
Rings.) 

119. Waves in the Surface of a Liquid. — When a liquid is 
heaped up it seeks to come to a level by gravity. It is not then 
a question of elasticity as the restoring force, hence waves 
produced under such conditions are called " gravitational 
waves." 



164 WAVES AND WAVE MOTION 

120. Rate of Travel of a Wave. — (a) Water waves. — If the 

water is of a depth greater than the wave length, and if the 
wave length is considerable, say, 10 cm. or more, it is found that 

the velocity of propagation is given by the equation v 2 = ^— » 

2 7T 

which is applicable to liquids of any density. In general, the 
velocity of waves in a liquid is given by v 2 = - — , where / is the 

2 7T 

acceleration due to the downward force and this consists of grav- 
ity plus surface tension. For gravity waves (where surface ten- 
sion is neglected) if r is the radius of the circle described by one 
particle, the wave length, X = 2 irr. It is found that the velocity 
of travel of the wave equals the velocity acquired by a body in fall- 
ing - r ; as r = — , this gives v = V — . Also, the time t, to travel 

2 27T T 27T 

the length of one wave, is - > 

v 

X 2 irr 

or /= — 7= = — ; — — = 2tt 






2jrr T g 

2 7T T 2 7T 

If T = the time of oscillation of a pendulum of length r, T = 2 t y -. 

y g 
Hence the time required for a gravitational wave to travel one 
wave length is the same as the time required for the complete 
oscillation of a pendulum whose length is the radius of a circle 
of which the circumference equals the wave length. (This is 
also the time required by a body to fall freely a height = w(2 wr), 
or 7rX, which is the circumference of a circle of which X is the 
diameter.) 

Illustrate by Lyman's wave apparatus, Fig. 72. 

But while gravity is in such cases the chief cause tending to 
restore the disturbed surface of the liquid to a level, there is also 
a pressure aiding this, due to surface tension. This pressure is 
greater the smaller the radius of curvature, and, as in long waves 
the radius of curvature is large, the effect of surface tension is so 



RATE OF TRAVEL OF A WAVE 



I6 5 



small relatively to that of gravity as to be negligible. The ex- 

2icT 



pression for the velocity due to surface tension is v 2 = 



Xp 



where T is the surface tension and p is the density of the liquid; 

. gX 2irT. 



and where both causes are taken into account tf 



+ 



2 7T Xp 

if the wave is very short, say, 0.4 cm. or less, the first term of the 
second member is negligible compared with the last. Such waves 
are called capillary waves or ripples. For more complete dis- 
cussion of liquid waves and ripples, see Encyclopaedia Britannica, 
Art. Capillarity; Watson's Physics, Arts. 270-273, 279, 280; 
Hastings and Beach, Arts. 476, 477. 

(b) Transverse Wave along a Stretched String. — Suppose the 
wave to be traveling along the cord from right to left with a 
speed v while the cord does not travel. So far as the forces in 
the cord are concerned it is the same as if the cord were made to 
travel from left to right at the rate v, and the crest of the wave 
remained at the same place. That would be the same as if the 

cord rested on the rim of 
a pulley whose radius R 
was the radius of curva- 
ture at A , and which was 
". rotating with a velocity 
of circumference equal 
to v, as in Fig. 78. 

Let m be the mass per 
unit length of the cord, 
and let BD represent a 
very short element of 
the cord, subtending an 
angle at C equal to 0. 
Then BD = Rd. That A should just keep its contact with 
the rim of the wheel, BD must be under a pull towards the 
center just equal to the centrifugal force upon it. If T is the 
tangential pull at each end of BD, i.e., the tension in the cord, 
each of these T's may be resolved into a component along 




Fig. 78. Travel of a Transverse Wave 
along a Cord. 



1 66 WAVES AND WAVE MOTION 

AC and another perpendicular to AC. The latter two neutral- 
ize each other, the former, added together, make the pressure 
toward the center. This centrally directed component of each 
is T sin J 6, or for both, 

2 T sin § 0. 

wiBDv 2 
The centrifugal force is — - — , and, equating, we have 

K 

— - — = 2 1 sin-^. 

R 2 

BD should represent an infinitesimal arc, for which sin J is 

iBD BD ^ , mBDv 2 T-BD . _ T 

- — — , or — — , therefore — - — = — - — , whence v 2 = — , or 
2 R 2 R R R m 



v = V — 



X —. That is, the velocity equals the square root of the 

quotient obtained by dividing the tension by the mass per unit 
length. In absolute units, taking T as dynes and m as grams 
per centimeter of length, v will be the velocity in centimeters per 
second. 

(c) A Longitudinal Wave in an Elastic Fluid. — The demon- 
stration for this is omitted as tedious though not too difficult. 
It is important, however, and students would do well to examine 
the demonstrations given in Hastings and Beach, General Physics, 
Art. 473, or in Watson's Physics, Art. 281. 

It is shown that the velocity is given by the equation v = y — 

(stress \ 
—) of the medium and 5 its 
strain/ 

density. Inasmuch as this expression for v does not involve the 
wave length, it follows that, in the same medium, waves of differ- 
ent length travel at the same rate. 

Examples. — 

1. A tidal wave 100 meters in length is started in mid-ocean, in what 
time will it arrive at a port 300 km. distant? (Art. 120(a).) 

Ans. 6f hrs. 

2. Ripples 3 mm. long are formed in the surface of mercury. If the 
surface tension of mercury is 540 dynes per centimeter, how fast do the 



RATE OF TRAVEL OF A WAVE 1 67 

ripples travel along the surface? How fast would ripples of the same length 
travel in water, surface tension being 81 dynes per centimeter? (Art. 
120(a).) Ans. In mercury, 28.8 cm./sec. 

In water, 41.2 cm./sec. 

3. A steel wire 100 meters long, 1 mm. in diameter, and of density 
8 g./c.c. has a weight of 2 kg. suspended from it; with what velocity 
will a transverse wave travel along the wire? If the wire is struck trans- 
versely at the lower end, in what time will the wave be felt at the top? 
(Art. 120 (6).) Ans. 55.86 m./sec; 1.8 sec. 

4. If the wire in Ex. 3 were suddenly jerked downwards at the lower end, 
at what rate would the impulse be transmitted, and in what time would 
it be felt at the top? (Art. 120 (c).) Take E = 20 X io 11 dynes per square 
centimeter. Ans. 5000 meters/sec. ; 0.02 sec. 



EXPERIMENTS TO ILLUSTRATE CHAPTER III. 

Experiment No. 48. Art. 113. Three Typical Wave Forms. 

In the Columbia wave apparatus (Fig. 79) three horizontal rows of 
particles are subject to the same periodic motion, any one particle being 
one eighth of a period in advance of the following one. 

In the upper row the particles describe circles and the line assumed by 




Fig. 79. Columbia Wave Apparatus. 

them at any instant has the form of a water wave, which progresses as the 
particles describe their circles. 

In the second row the particles are constrained to move only to and fro 
in the same line with the particles, giving the form at any instant of a sound 
wave which is a wave of condensation and rarefaction, that moves along as 
the particles vibrate. 

In the third row the particles are constrained to move only in a direction 
transverse to the line of the particles, giving the form of ether, or light waves, 
the wave traveling along the horizontal line while the vibration is vertical. 
Experiment No. 4Q, Art. 116. Nodes and Loops of Stationary Waves. 

Attach an elastic cord, as, e.g., a coiled wire, 3 or 4 meters in length, to 
a hook in the wall, and, drawing the cord moderately tight, send waves along 
it by shaking the end. With care, the cord may be thrown into vibration 
with stationary waves, showing one, two, or even half a dozen segments. 

Experiment No. 50, Art. 117. Interference of Waves. 
A shallow dish (Fig. 80) of elliptical or other suitable geometric form, 
contains mercury. A funnel tube is drawn out to a fine opening, placed 
over one focus of the ellipse, and mercury is poured into the funnel. The 

168 



EXPERIMENTS 



169 



drops form waves which proceed as circles expanding from one focus and 

converging upon the other, which point in turn acts as an origin of waves, 

and these, crossing the set from the 
first focus, produce distinct bands 
of reenforcement and interference, 
showing as secondary ellipses in the 
surface of the mercury. 

The waves may be excited by 
means of a slender iron stylus at- 
tached to the end of one prong of 
an electrically driven tuning fork. 
Even without the funnel dropper or 
the stylus, the mercury surface will 

show the waves, foci, and interference by tapping with the knuckles on the 

vessel containing the mercury, or simply on the table on which the dish 

stands. 

With an opaque projection apparatus they can be shown upon a screen, 

or upon the ceiling by an ordinary large convex lens, in the reflected beam 

of nearly parallel light from a lantern. 




Fig. 80. Interference of Liquid Waves. 



CHAPTER IV. 

SOUND. 

121. Sound as a Phenomenon and as a Sensation. — The 

word "sound" is used to express a physical fact as well as a mental 
perception. It may be considered, therefore, both objectively 
and subjectively. It is with the former view that physics has 
to do chiefly. 

122. Sound a Wave Phenomenon. — Sound should be classed 
among wave phenomena because it obviously requires time for 
its transmission, and there is abundant evidence that it is periodic 
in character. A sounding body is always a vibrating body: it 
may be a solid, as a bell; a liquid, as a waterfall; or a gas, as the 
wind; or the siren, or wind instruments of music, though the last 
are assisted by casing of thin solid. A vibrating body is not 
necessarily a sounding one, at least it may not be audible, but 
vibration is the only difference necessary to convert a silent body 
into a sounding one, and neither in the body that is causing the 
sound, nor in the medium transmitting it, is any change per- 
ceptible except vibration. 

123. Complexity of Sound Phenomena. — 
For the production of sound, then, vibration is 

essential. 

Mechanical < For the transmission of sound is needed a me- 
dium capable of receiving the vibrations and 
impressing them on the ear. 
fFor the reception of sound is required an organ 
' ' [ of hearing, as the ear, or teeth and nerves. 

. fFor the perception of sound is needed the brain 
[to act in response to the nerves. 

Thus the complete consideration of sound (as also that of light) 

involves three processes. 

170 



SOUND DUE TO LONGITUDINAL VIBRATION 171 

Experiment No. 51, page 199. — Necessity of medium for conveyance 
of sound is shown by bell under receiver of air pump. 

Observe especially that the medium which brings the vibra- 
tions to the ear and actuates the organ of hearing is that in 
which the ear is embedded, as air or water, and not the ether. 
Sound failed by removal of air from the receiver though ether was 
still there. 

A distinction is sometimes made between sound and noise. 
Where such a distinction is employed, sound results from a series 
of regular vibrations or a combination of such regular vibrations 
as have frequencies related to one another in simple ratios; 
noise results from a jumbling of abrupt single impulses having 
no definite numerical relation to one another. 

It may be called sound if the action is sustained only long 
enough to give to the ear a sense of rhythm. 

Experiment No. 52, page 199. — Illustrate sound and noise by the grad- 
uated blocks of wood. 

Vibration of an elastic body (or medium) takes place in 
obedience to a force of restitution that is proportional to dis- 
placement; the motion therefore is S.H.M. 

124. Sound Due to Longitudinal Vibration. — Whatever the 
character of the vibration that is to result as sound, whether 
the vibrating body is itself vibrating transversely or longitudi- 
nally, the wave that finally affects the ear is one of compression 
and rarefaction. A stretched string may itself vibrate trans- 
versely, and in so doing may be scarcely audible; if it is heard 
at all it is by means of compression and rarefaction which it 
produces in the air, and which will be slight because there is but 
little surface to the vibrating string to disturb the air; but if the 
string is so mounted as to set vibrating a larger surface like a 
sounding board the sound is more pronounced. A rod may be 
set vibrating transversely, but its vibrations will constitute sound 
only when the transverse vibrations have been converted into 
longitudinal ones either in the rod itself or in the subsequent 
media. If the rod is stroked longitudinally it is at once set 
vibrating longitudinally. 



172 SOUND 

Experiment No. 53, page 199. — A sensitive flame shows the variations 
in pressure at the orifice of the gas jet. 

Experiment No. 54, page 200. — Projecting a Crova's disk upon the 
screen shows the actual formation and progress of sound waves. 

125. Velocity of Sound. — The velocity with which sound 
will travel, then, in any medium is the velocity of propagation 
of a compressural wave in that medium. This velocity, for any 
homogeneous elastic medium, was shown by Newton to be 
"E 



\/ 



N see Art. 120(c)), where E is the measure of the elasticity 

of the medium and 8 is its density. Note that E and 8 are the 
elasticity and density of the medium in which the sound is travel- 
ing, which usually is not the vibrating body from which the sound 
is proceeding. 

For transmission in a long narrow body as a wire, the elasticity 
E is simply Young's modulus, but for a fluid it is necessary to 
use the volume elasticity. That is the ratio which the stress (or 
increment of pressure per unit of area pressed) bears to the strain 
produced by that increment of pressure, and the strain is the 
ratio which the diminution of volume bears to the original 
volume. If V is the initial volume of the fluid, p the additional 
pressure per unit of area applied and v the diminution in volume, 

v . v fiV 

then p is the stress, — : is the strain and E = p -7- — = iL — • For 
V V v 

water at 4 C. the density is 1 ; an increase of pressure equal 
to one atmosphere or 76 cm. of mercury (1,013,300 dynes per 
square centimeter) diminishes the volume 0.000049 part. Then 

r, 1,013,300 . , 

stress = 1,013,300, strain = 0.000049, h = — - — > 8 = 1 and 

' °'° ' _' 0.000049 

velocity of sound in water = \ — = 143,800 cm./sec. 

T 8 

Various experimental determinations for water at slightly 
higher temperatures give a velocity of about 143,500 cm./sec. 

In a similar manner the velocity of sound in any other liquid 
may be determined. Owing to the minute compression and the 
high specific heat of liquids their temperature in transmitting 
sound waves undergoes practically no change. 



VELOCITY OF SOUND 1 73 

In a gas at constant temperature, as we have seen (Art. 59), 
the elasticity is equal to the pressure. For air at o° C. and stand- 
ard barometer pressure, 8 = 0.001293, and E = 1,013,300, and 

these in the formula v = \ — give, for the velocity of sound, 

8 

27,995 cm./sec. As compared with experimental determination 
of the velocity of sound in air under those conditions, this is in 
error by 20%, the true value being 331.3 m./sec, an error quite 
too large to be ascribed to fault in experimentation, and showing 
that there is some fundamental error in the formula itself or in 
its derivation. 

In a gas the temperature changes considerably with moderate 
changes of pressure, and as the elasticity equals the pressure only 
for constant temperature, it is in the effect of temperature upon 
the elasticity that we should first look for the error. Now if the 
changes from condensation to rarefaction and the reverse through 
the initial condition take place too rapidly for the heat to be 
carried from or to the portion of gas affected, the changes of 
density are occurring adiabatically, and the elasticity of the gas 
is not equal to the pressure. In Art. 108 it was seen that in an 
adiabatic change of a gas, PV k = constant. Now if P is in- 
creased by the small pressure p, the volume of gas will be dimin- 
ished by the small quantity v, and we shall have 

PV k =(P+p)(V-v) k 

and, by expanding (V — v) k and neglecting the higher powers of v, 

PV k = (P + p)(V k - kV k ~ l v) 

= PV k - kPV k ~h + pV k - kV k - l pv, 

and, omitting the term containing the product of the two very 
small quantities p, v, we get 

_pV 



kPV k ~h = pV k or IP 



v 



pV 
But it has just been shown above that ^— = E\ therefore in 

v 

adiabatic compression and rarefaction of a gas E = kP (see 



174 SOUND 

also Watson, Art. 287), and in this view we may write for the 



\l kF 



velocity of sound in a gas, v = y — k is the ratio of the specific 

* 8 

heats of the gas, and for air is found to be 1.41. This gives for 

/ P 

sound in air at o° C, v =\ 1.41 — = 332 m./sec, agreeing very 

? 8 

closely with experiment. 

This correction, due to Laplace, seems so far warranted that 
it is now taken as the best means of determining the ratio of the 
two specific heats of any gas. The velocity of sound in the gas 
at a given pressure and density can be determined, and from the 
above formula for v the value of k is computed. 

(See Watson, Art. 287, for the effect of pressure upon the 
velocity of sound in a gas for which Boyle's law does not hold; 
that is, for gases when near the point of liquefaction.) 

126. Effect of Temperature on Velocity of Sound in a Gas. — 
If a gas is so rare as practically to conform to Boyle's law, 
then any increase of pressure decreases the volume or increases 
the density in exactly the same proportion if the temperature is 

IkP . P . 

not altered, so that in the formula v = V — ■ > the ratio of — is not 

y 8 8 

affected by change of pressure for any given temperature; but 

under any pressure whatever, a change in temperature changes 

the density inversely per degree, as much as the coefficient of 

expansion, say a, so that if v is the velocity in air at o° C, and 

8 is its density, at any temperature f the density will be 

5 

I + at' 



and v t = V "T ( z + at ^ 

1 8 



==V Vi-Jr at, 

in which, for air, a = 0.003665. With a rise of one degree in 
temperature, the velocity of sound in air is Vi. 003665 times that 
at o° C, an increase of 60 cm./sec. 



THREE CHARACTERISTICS OF A SOUND; PITCH 1 75 

As in wave motion generally, if X is the distance the disturb- 
ance travels in the time of one vibration, it is the length of one 
wave; and if n is the frequency of vibration, i.e., the number of 
vibrations per second, then the velocity v is equal to n\ ; or if T 

is the time of one vibration, n — — , and v = —. In these equa- 
tions either quantity may be expressed in terms of the other two. 
(For consideration of the subject of the last two articles in 
connection with the kinetic theory, see Daniell's Physics, Art. 
" Propagation of Sound in Gases according to Kinetic Theory.") 

Examples. — 

i . Taking the velocity of sound in air at o° C. as 33 1 .3 meters per second, 
what will be the velocity at 20 C? Ans. 343.2 meters per sec. 

2. When the temperature of the air is o° C. the steam escaping on blow- 
ing the whistle of a locomotive is seen three seconds before the sound is 
heard; how far is the observer from the engine? Ans. 994 meters. 

3. How much time would be required for the sound to reach the observer 
if the temperature were 30 C? Ans. 2.8+ sees. 

4. An obstruction in a pneumatic mail tube was located by discharging 
a pistol in front of a membrane stretched across the open end of the tube, 
and observing accurately when the pulse that traveled along the pipe 
was returned to the open end after reflection from the obstruction. If 
this time was 2.25 seconds and the temperature of the air in the pipe was 
20 C, how far from the open end was the obstruction? 

Ans. 386.1 meters. 

127. Three Characteristics of a Sound. — Sounds other than 
those so confused as to be termed noise are distinguished by the 
three characteristics pitch, intensity (or loudness) and quality 
(or timbre). Variation of either of these attributes without 
regard to the others will cause a perceptible difference in the 
sound, easily recognized by the ear and determinable by physical 
measurement. 

128. Pitch. — The difference between one note and another 
in pitch is that difference which is usually expressed by high or 
low (not loud or soft). One note may be loud and another 
scarcely audible, yet they may both be of the same pitch, and if 



I7& SOUND 

a note sounded by a musical instrument is repeated by the voice, 
the sound of the voice will probably differ greatly from that of 
the instrument except that it will have the same pitch, and will 
then be said to be in tune with it. The pitch, that is to say the 
highness or lowness of a tone, has reference solely to the rate 
or frequency of vibration, the number of vibrations per second 
producing it. This may be shown to be a fact, and at the same 
time the actual number of vibrations corresponding to any pitch 
may be determined by a suitable counting apparatus. 

Experiment No. 55, page 200. — The siren determines it by counting the 
puffs of air; Savart's wheel, by the taps on the teeth of a wheel; different 
tuning forks, by tracing their vibrations on a smoked surface. 

129. Musical Scale; Intervals. — A musical ear recognizes 
distinctly notes of different pitch as differing in the same de- 
gree and manner, when they have the same relative rates of 
vibration, no matter what their actual rates may be. The differ- 
ence in pitch, then, of two sounds is expressed not by the arith- 
metical difference in their rates of vibration, but by the ratio of 
their frequencies, and this difference in pitch is called the interval 
between the tones, the ratio of the vibration rates being the 
measure of the interval. Not only is the interval recognizable 
when the notes are sounded in succession, but the effect of sound- 
ing two together depends for its smoothness or pleasantness upon 
the interval between them. If one note has a frequency twice as 
great as another, the interval between them is 2, and this interval 
is called an octave. It makes no difference what the actual 
frequency of one may be ; if it is one half or double that of the 
other, they are separated by an interval of an octave. Between 
a given note and its octave above, the ear accepts naturally 
a number of intermediate intervals rising in successive simple 
ratios with the first frequency, and forming a so-called natural 
or diatonic scale. If we call the first note the unit, then the 
rates of vibration or the intervals within the octave are as follows, 
the first line being the common names of the notes, the second the 
intervals between each note and the first, and the third line 
the intervals between the successive notes: 



MUSICAL SCALE; INTERVALS 1 77 

do re mi fa sol la si do 

T 9 5 4 3 5. 1_5_ 

1 "8 4 3 2 3 8 z 

9 1_0 JL6. 9. 1_0 9 16_ 

8" 9" 15 8 9 8 15 

These seven steps are seen to be not quite equal although the first, 
second, fourth, fifth and sixth, are nearly so and are called whole 
tones, while the third and seventh are smaller and are called half 
tones or semitones. 

It may seem queer that a gamut of seven steps in intervals 
so irregular should be a " natural scale." This irregularity is 
easily shown to be simply the mathematical result of shifting 
the beginning note, to form sets of notes in simple ratios. 
Nothing is more common in sound than the production of' an 
octave up or down, and this means doubling or halving the initial 
frequency. Three notes whose vibration rates are as 4 : 5 : 6 
make an agreeable combination, forming a (major) natural 
triad. Why this combination should be natural or agreeable 
we cannot tell, though the fact has been discussed, notably 
by Pythagoras among ancient philosophers, and by Euler and 
others among the moderns, but their views are chiefly specu- 
lations. 

If we start with a note of definite pitch which we may call 
C and its frequency the unit or 1, the triad will be numerically 
1 : f : I, 2 being the octave. If we produce a like triad beginning 
with the third one of this series, the numbers will be as f : f X f 
: f X f, or f : \ 5 - : f ; and if we insert a similar set of which 
the octave 2 shall be the uppermost, this triad will be numer- 
ically f : I : 2 as these are in the ratio 4:5:6. We now have 
from our beginning note C = 1, intervals built up from the 
ratios 4 : 5 : 6, as follows: 



D E F G A B 

5 . 4 . 3. . 5 . 15 

4 • 3 • 2 • 3 • 8" 



I ' ( ) ' 



The octave below the last of these is f, occurring between 
C and E, in the parenthesis, and completing the scale of seven 
intervals in the octave from C to c. 



178 SOUND 

130. Temperament. — The scale might begin with a note of 
any frequency and progress by the intervals just given. As the 
interval between the third and fourth notes is called a half tone, 
and equals y§, the whole tone intervals might each be subdivided 
into half tones, making twelve intervals in the octave, but two 
successive intervals of ^f would not make a rise of exactly f , for 
if X xf equals 1.138 instead of 1. 12 5. If we letter the notes 
of the scale C, D, E, F, G, A, B, c, the half tone above C would 
be called C sharp (C #) , and a half tone below D would be properly 
D flat (Db), and, allowing ^| for a half tone, C# would be higher 
than D b. Again if absolute numerical values were given for the 
pitch of the notes according to the natural intervals, beginning 
the scale with C, then those numbers would not make the correct 
intervals if we wanted to begin with C# or D. An instrument 
with fixed pitch for each key that is struck, like a piano, would 
require an enormous number of sets of keys and strings or pipes 
to make music with true intervals in different "keys" (i.e., 
starting the octave with different frequencies as the keynote). 
With an instrument like a violin on which a note of any pitch may 
be produced, this is not the case. 

To escape this difficulty, scales have been adopted in which 
some of the intervals have been made slightly false. A scale thus 
altered is called a tempered scale. The mode of tempering 
almost universal now is to make an even-tempered scale or scale 
of equal (or "just") temperament. This is produced by choos- 
ing some value for one of the notes and then dividing the octave, 
for which the whole interval is 2, into twelve equal intervals of 
^/2, or 1.059 e ach. That makes some of the notes a little too 
high and others a little too low, the actual comparison being as 
follows : 
Natural scale, 1; 1.125; 1.25; 1.333; 1 -5 J 1-667; 1.875; 2 - 

S^nLmPTit \ i; 1 ' 12 '' I>26; I,325; I498; I>682; I,882; 2 * 

temperament 1 CD ef G A Be 

In ordinary conversation the voice is modulated in musical inter- 
vals, the most frequent being the octave with which the final 
word of an assertion is uttered, the voice dropping or rising 



DOPPLER'S PRINCIPLE 1 79 

through an octave involuntarily. It is interesting thus to ex- 
amine the intervals in the modulation of the voice by different 
speakers. (Illustrate.) 

Stage recitation is sometimes done to music, making it difficult some- 
times for the listener to decide whether the performer is speaking or 
singing. 

A musical voice is one in which the sound is neither harsh nor 
husky, and which is so modulated that the intervals in its tones 
are exact. 

The International Standard Pitch gives the middle A of the 
pianoforte 435 vibrations per second, from which, by natural 
intervals, the c above it would have 522 vibrations per second, 
but by equal temperament it has 517.3, and this latter number 
would be the proper frequency for a c fork to be used in tuning 
for an even tempered scale with the International Standard 
Pitch. The New York Philharmonic Society uses the Stuttgart 
Standard for which A has a frequency of 440 vibrations per 
second. 

Example. — Starting with the middle C of the pianoforte as 260 vibra- 
tions per second, the pitch of an octave above E was fixed by equal tem- 
perament, and from this the note c (i.e., the octave above C) was deduced 
on the natural scale; how much did it differ from the piano? 

Ans. 4.12 vibrations per sec. higher. 

131. Doppler's Principle. — The pitch of the note issued by 
a sounding body is determined by the rate of vibration of the 
body; the pitch of the note perceived by the ear is that due to 
the number of vibrations per second received by the ear, and 
these two pitches are not necessarily alike. If a body sends out 
n waves per second, and the source of sound and the ear are at 
a constant distance apart, the medium transmitting the waves 
being at rest, then the ear will continually receive n waves 
per second, but if the ear and the sounding body are approach- 
ing each other the ear will receive more than n waves per 
second and the pitch will be higher, or, if they are separating, 
the ear will receive fewer than n waves per second and the 
pitch will be lower. Suppose the velocity of sound is V and the 



180 SOUND 

sounding body (supposed to be stationary) is emitting n waves 

. v 

per second. The wave length X is — . If the observer is station- 

n 

ary he will receive n waves per second, but if he moves toward 

the sounding body a distance v per second, he will in this distance 

v 
increase the number of waves he receives by - , so that, in all, he 

A 

receives in one second n + -, or» + -, that is, n ( i + j). In 

X V \ v J 

the same way, if he is receding from the source of sound at a rate 

v 
v, he will receive in one second n — - , and the pitch of the note 

X 



will be 



K 1 -?} 



This change of pitch and its explanation are known as Doppler's 
Principle. It has important applications in connection with 
light. Other changes of pitch ensue when the transmitting medium 
is in motion. See Barton's Text Book of Sound, Arts. 60, 61. 

Example (from Watson's Physics.) — "A locomotive whistle emitting 
2000 waves per second is moving towards you at the rate of 60 miles per 
hour on a day when the thermometer stands at 15 C. Calculate the appar- 
ent pitch of the whistle." 

Velocity of sound at o° = 1093 ft./sec. 
V = 1093 Vi + 0.003665 X 15 = 1122.5 

v 
60 miles per hour is 88 ft./sec. = v and — = 0.0784. 

Apparent pitch = 2000 X 1.0784 = 2156.8. 

Curious results are deducible for cases in which the body pro- 
ducing the waves is moving at the same time faster than the 
waves themselves travel. (See Watson, Art. 299.) 

132. Velocity of Sound Independent of Pitch. — The formula 
for the velocity of a compressural wave (Art. 118) is independ- 
ent of the rate of vibration, thus indicating that waves of 
all frequencies progress with the same speed. This is verified 
in the case of sound waves. Notes of different pitch travel with 
the same velocity, as is evidenced by the fact that notes in a 
musical performance played in definite time, following upon one 



INTENSITY OF SOUND 181 

another in well denned periods, follow each other in just the same 

periods when the music is heard at a long distance from where it is 

produced. 

If, then, v is the velocity of sound for all frequencies, and n is 

the frequency and X the wave length for any given note, n such 

i) 
lengths make the distance v, or v = n\, or X = - • 

n 

133. Intensity of Sound. — A note of any pitch may be 
strong or feeble, the difference in this respect being called a 
difference in intensity, and the difference of sensation produced 
is a difference in loudness. The intensity does not depend upon 
the frequency, but upon the energy of vibration. In general the 
energy of vibration for any body is proportional to the square of 
the amplitude of vibration, so that the intensity of sound pro- 
duced by a given body will vary as the square of the amplitude 
of its vibration; but if the same body be so mounted as to expend 
its energy upon a limited mass of the conveying medium, as the 
air in a tube, instead of dissipating it in a large sphere of air, 
the sound at the end of the tube will be more intense than at that 
distance in air unconfmed. Again, if the vibrating (or sounding) 
body is mounted upon a sounding board or box, its energy is 
applied to disturb a greater mass of the air near it, and the sound 
at a distance is correspondingly more intense. It is plain that 
in such case the vibrations of the body will die out sooner, or its 
energy be sooner exhausted, than if it were agitating less mass. 
(Illustrate by tuning forks: small one in air, scarcely audible; on 
table, plainly heard.) 

That the pitch remains the same while the intensity dimin- 
ishes, and that the intensity falls off with a decrease in the ampli- 
tude of vibration, may be shown by successive tracings of the 
vibrations of a tuning fork as the sound dies out. 

The energy of vibration of air in the bounding surface of a 
sphere can be shown to decrease as the square of the distance 
from the source of vibration increases, and so the physical inten- 
sity of sound varies inversely as the square of the distance (Wat- 
son, Arts. 312, 313), but the loudness, which is a physiological 



182 SOUND 

sensation, does not vary in any such definite proportion, though 
it does increase with an increase in intensity. 

134. Quality of Sound; Overtones. — There is a rate of 
vibration for every body that may be called its natural or normal 
rate, and which is the slowest rate at which it will vibrate 
without constraint. This evidently depends upon the nature 
of the material and upon the form and dimensions of the body. 
The tone which it emits when vibrating in its lowest frequency 
is called its fundamental tone. Most bodies, however, are capa- 
ble of being put into other and higher rates of vibration, 
by dividing up into vibrating segments, and the tones due 
to these more rapid vibrations are called overtones. If a 
body is emitting at the same time its fundamental and over- 
tones along with it, the effect, to the ear, is different from 
that due to the fundamental alone, although the pitch would 
be said to be the same in both cases. This difference is called 
a difference in quality {timbre, Klang-farbe) . The lowest rate 
of' vibration present in the note determines the pitch. If the 
frequencies of the overtones are those obtained by multiplying 
that of the fundamental by the natural numbers 2, 3, 4, . . ., 
they are called harmonics. The actual quality of the tone is 
determined by the particular overtones that are present with 
the fundamental, and their respective intensities. An analysis 
of sound consists, for the most part, in resolving a compound 
tone into its constituents and determining them. 

Experiments Nos. 56 and 57, page 201. — Composite vibrations of sound 
shown by manometric flames; fundamentals and overtones produced with 
tuning forks. 

135. Reflection and Interference of Sound. — Sound waves 
undergo the changes due to reflection, interference, etc., that 
have already been presented in considering wave motion; the 
most familiar illustration of reflection of sound being the echo. 
If sound travels, say, 340 meters per second, then a sound from 
a point opposite a wall that is at a distance of 170 meters will 
return to the source in just one second. If various sounds 
were being produced at intervals of one second, the echo would 



LONGITUDINAL VIBRATION OF RODS 183 

cause confusion. At one tenth the distance (or about 55 feet), 
sounds emitted at the rate of ten a second would be in confusion 
with the echo, and articulation would be indistinct. This would 
also be the case at any point in a room where the echo of one 
sound arrived at the same instant that a succeeding sound arrived 
in its direct path. Failure to recognize these principles is re- 
sponsible for a good deal of the bad acoustics of halls intended 
for public speaking. In the construction of such halls such 
arches or domes in the ceiling as would produce focal regions or 
axial focal lines in the audience by reflection of waves proceed- 
ing from the rostrum should be especially avoided. 

A sound wave traveling in one medium and arriving at the 
surface of a second medium of different density is reflected in 
part, if not wholly, and if the reflecting surface is perpendicular 
to the line of progress of the waves, the reflected waves directly 
retrace the path of the advancing waves and interference will 
result. That is, at regular intervals, where the motion of the 
advancing waves would crowd the particles, say, to the left, that 
in the reflected waves would crowd them toward the right and 
there would be stationary particles in condensation; half a wave 
length further along there would again be stationary particles 
due to a tendency to separate in both directions; half a period 
later the former of these places would still be a place of rest but 
of rarefaction, while the latter would be in rest but in conden- 
sation. In fact these places would be permanently places of 
rest due to interference, while between them would be places of 
maximum motion alternately in one direction and in the opposite. 
This is a case of stationary waves of sound, the points of no 
motion, or rather of minimum motion, being nodes, and between 
them loops, the distance from node to node or from loop to loop 
being half a wave length.' 

Example. — With the temperature of the air 20 C, a man standing 
some distance from the face of a cliff fires a pistol and hears the echo two 
seconds later. How far is he from the cliff? Ans. 343 meters. 

136. Longitudinal Vibration of Rods. — The elasticity and 
density of a rod will determine the speed with which a sound 



1 84 SOUND 

wave will travel along it. If the rod is fixed at one end and free 
at the other, then when the rod is stroked the fixed end is neces- 
sarily at a node and the free end at a loop. The longest wave 
the rod can then represent will be four times the length of the 
rod itself, and, v being the velocity of sound in the material, the 

v 
frequency of vibration will be — • If the rod is clamped in the 

4/ 

middle and free at the ends, the mid-point will be a node and 

each end a loop. The length / of the rod is then half a wave 

length or -, the wave length is 2 I, and the pitch is that of n 

2 

v 
vibrations where n = — . By means of these formulae, if the 
2 / 

pitch of the note is determined, the velocity is at once calculable, 
and from the measured density the elasticity may be found ; or, 
with rods of different material tuned to the same pitch, if the 
densities are known the values of E may be compared. Let n, 
E, 8 and / represent respectively the frequency, elasticity, den- 
sity and length of rod, then 



= y -~ and n 2 = \f ~r 



5, £ 



2/1 2/2 

If these values of n are equal, since 5i, 5 2 , h, h are known, the 
ratio of E x to E 2 becomes known. 

Example. — An iron rod having a mass of 92.7 g., length 80.5 cm., 

diameter 0.436 cm., when held in the middle by the thumb and forefinger 

and gently stroked with a rosined piece of chamois, emitted a note that was 

the third octave above the G of an adjustable tuning fork. The frequency 

of this G was 389 vibrations per second. The pitch of the note emitted by 

the rod, therefore, was n = 389 X2X2X2 = 3ii2. 

X = 80.5 X 2 = 161 and v = 161 X 3112 

= 501,000 cm. /sec. 

at ,. mass 92.7 , 

Also 5 = — = v = 7-73 g./cc. 

volume n.994 



= v/-> 



and since d=V/-, E = z> 2 5 = 193 X 10 



sq. cm. 
200 X io 4 kg./sq. cm., nearly. 



INTERFERENCE 



185 



137. Kundt's Tube. — By inclosing air or any gas as a col- 
umn in a tube so that the length of the column can be adjusted, 
and inserting a rod of metal carrying a loosely fitting piston 
at the end in the tube while half the rod or more extends outside 
the tube, stroking the rod while it is held firmly at its middle 
point puts it into longitudinal vibration, and the light piston 
on the end of the rod imposes waves of condensation and rare- 
faction of the same period upon the column of inclosed gas. v 
being the velocity of sound in the gas and n the frequency of 

v 
vibration, the wave length in the gas of such waves is - ; a half 



wave length is — . If the length of the air column is divisible 

2 n 

by this number it will break up into segments of this length. 

Experiment No. 58, page 202. — Kundt's tube experiment. 
138. Interference. Can Two Sounds Produce Silence? — 
Stationary waves are due to interference of reflected with ad- 
vancing waves. These two trains may be regarded as proceed- 
ing from two different sources, though in fact all originating at 
the same source. It is possible, however, so to employ two 
different sources of sound that the waves will interfere at definite 
places. If a wave proceeding 
from one source arrive at a cer- 
tain point in a phase, say, of 
condensation, and a wave of 
equal intensity from another 
source arrives at the same point 
in a phase of rarefaction, the 
effect of the two at that point 
will be nil. If, furthermore, 
the sounds are of the same 
pitch (i.e., frequency), this 
place will be one of continuous 
silence. One of the simplest 
illustrations of interference of sound waves is with an ordinary 
tuning fork. Suppose (Fig. 81) to be between the ends of a 




Fig. 81. Interference of Sound Waves. 



1 86 SOUND 

vibrating tuning fork. The prongs alternately approach each 
other and recede, causing the air between them to be alternately 
condensed and rarefied, while that at the back of them is at the 
same time alternately rarefied and condensed. A series of waves 
will proceed outward, represented in the plane of the paper by 
heavy (condensed) and dotted (rarefied) circles. At four points 
around each circle there will be a tendency at the same instant to 
both condensation and rarefaction, and interference will be pro- 
duced along the lines 10 K and I'OK' . Such a vibrating fork 
held vertically before the ear and slowly rotated will give four 
distinct positions of silence in one rotation of the fork. 

139. Resonance. — Strictly speaking, resonance could only 
apply to sound, for it would be impossible for any body to be 
resonant unless it or some other body were first sonant, but the 
similarity of occurrences in other branches of physics to those 
in acoustics has warranted an extension of the term to cases in 
which sound plays no part. 

If any rhythmic action in one body excites in another, whether 
directly connected with the first or apparently disconnected from 
it, rhythmic action of like periodicity, the second body is said 
to be in resonance with the first. 

In the case of sound the body that is primarily vibrating may 
be emitting but a feeble sound, but may awaken such vibrations 
in an inclosed air space as to make a loud sound. Such a space 
is called a resonance chamber or resonator, and the air in it a 
resonance column. If a large surface of solid or liquid has been 
put into vibration it is called a sounding board. 

To resound to a note of given pitch the resonance column must 
be of proper dimensions to vibrate at the rate corresponding to 
that pitch. A column of air in a tall vessel AD (Fig. 82) will 
resound to a fork vibrating above it if the wave after reflection 
from a surface, as B, arrives at the mouth A in such phase as is 
then being produced there by the vibrating fork. When the tine 
T begins to move downward it starts a pulse of condensation 
down the tube; this, arriving at B, is there reflected and returns 
to A. If it reaches A when the prong of the fork is just ready 



RESONANCE 



187 






> 



to return the pulse must travel 
from A to B and back while the 
prong of the fork swings from 
T to T 7 , or the time is one half 
the period of vibration. From 
A to B and back would then be 
one half the length of the sound 
wave in air. 

The prong of the fork, how- 
ever, will be starting in the oppo- 
site direction from that in which 
it was going when it sent the 
pulse down the tube, in one half 
a period, or in §, or |, or any odd 
number of half periods. If the 
returning pulse is in time with 
any of these returns of the fork, 
resonance will occur. That is, 
the distance from A to B and back must be an odd number of 
half wave lengths, or AB must be an odd number of quarter wave 
lengths. If the distance from A to the reflecting surface B, B h 

B 2 , etc., is /, the column will resound if I = (2 x + 1)-, where x 

4 
is any number, and X is the wave length for the pitch of fork 
used. The simplest and strongest resonance occurs for x = o, or 
AB = one quarter- wave-length. When the value of x is known, 
and also the rate of vibration of the fork, the velocity of sound 

v 
in the gas in the tube can be determined, for X= — , and therefore 



Fig. 82. Resonance of Air Column. 



/ = (2 x + 1) — - . For the first or fundamental resonance, x = o, 
411 

and v = 4 nl; for the next resonance, i.e., for the next greater 



37; 



4 nl 



length of tube, AB h x = 1, and I = — , whence v = 

\n 3 



and 



so on, 



Owing to the spherical form which a wave assumes as it 



1 88 SOUND 

proceeds from a point of disturbance, and also probably on 
account of some retardation by friction along the sides of the 
tube, the wave front of air at the mouth A is curved somewhat 
upwards, so that the actual length to be counted for -J X is AB 
increased by a quantity that varies somewhat with the diameter 
of the tube, from 0.6 to 0.8 of the radius. 

Experiment No. 5p, page 202. — Resonance of tube with adjustable 
water column. 

The whistling of a key, or of the cap of a fountain pen, and the 
popping of a bottle when uncorked are instances of resonance. 

Pitch of Nature. — The general contour of the country, the presence of 
trees, brooks and houses, the varied occupations of men, the movement 
of machinery, all combine to produce in the ear of a listener a dominant 
tone of which the pitch may be identified. 

At Dorollis, N. Y., in August, 1910, the wind in the trees and the humming 
sound made up of this, and the murmuring of the brook, and other noises, 
which, with their reverberation from the hills, combined to make up the tone 
of nature, produced a note of which the pitch was a half tone under the octave 
below the note emitted by the cap of a fountain pen. The cap was 1 cm. 
in diameter and 5.9 cm. deep. Adding 0.35 to 5.9 gives 6.25 cm. for one 
quarter wave length, or 25 cm. as the wave length of the note it emits. At 
20 C. the velocity of sound is 342 m. per second, and the pitch of the note 

from the cap is — , or 1368 vibrations per second; about the third F 

25 
above middle of pianoforte scale. The octave below this is 684 vibrations 

per second, and the half tone under that is 684 -7- 1.059, or 645, which was 
the "pitch of nature" as then observed, approximately the second E above 
the middle C of the piano. 

On Jan. 18, 1908, in City Hall Park, New York City, between the City Hall 
and the Court House, with Park Row and the clamor of the other streets and 
the Brooklyn Bridge terminal on the east and Broadway on the west, the sounds 
from the east seemed to reduce to a note of 940 vibrations per second, while 
the sound from the west or Broadway side was one full tone lower, corre- 
sponding to 840 vibrations per second. 

Forks for experimentation are mounted on resonance boxes 
closed at one end and open at the other. These boxes are usually 

of a length that is approximately - for the period of the fork they 

4 

carry (somewhat less than - on account of their width). The 



RESONANCE CHAMBER 189 

fork vibrating on the cover of the box has its vibrations trans- 
mitted to the air within by the elasticity of the cover, but if the 
fork be dismounted and held, while vibrating, before the mouth 
of the box, the resonance is pronounced. (The hole in the top 
of the cover must be stopped.) Here the interference effect 
described in Art. 138 is plainly shown by rotating the fork before 
the mouth of the resonance box. 

Experiment No. 60, page 203. — Interference of sound. 

It is to be noticed that a given resonance chamber will not 
resound to all tones, but only to those of a certain period, and 
first and most forcibly to its fundamental tone. Perhaps the 
most remarkable resonance cavity is that which sustains the 
voice and is formed by the mouth, throat and nasal passages. 
The variations in its size and form by the muscular action of the 
person speaking or singing accounts for nearly the whole range 
of modification which vocal sounds receive. The vibrations pro- 
ducing the sound are due chiefly to the vocal cords and the lips, 
but the variations in tone are due to the resonance qualities of 
this chamber. 

An interesting illustration of complex vibration in a single 
elastic rod and the facile action of the mouth in resounding is 
shown by the jew's-harp. (Illustrate.) 

There is, then, a pitch of voice to which any room or hall readily 
responds. A speaker using this as the dominant pitch in speak- 
ing feels his voice strengthened or sustained, and a skillful elocu- 
tionist readily discovers the pitch appropriate to the hall in 
which he speaks. The same room, when filled with people, may 
call for a different pitch of voice from that to which it resounds 
when empty. 

Examples. — 

1. The fork above the tall vessel in Fig. 82 makes 320 vibrations per 
second, and gives strongest resonance when the air column AB is 25.4 cm. 
long. If the diameter of the vessel is 4 cm., what is the velocity of sound? 
What length of air column AB would give the next resonance? (Add 
o.yr to AB for Jx). Ans. 343 m./sec; 79 cm. 

2. A shrill note is produced by blowing across the end of a key. If the 



190 SOUND 

bore is 3 mm. in diameter and 1.2 cm. deep, the velocity of sound being 
345 meters per second, what is the frequency of the note emitted? (Add 
o.8r to depth of bore for |X.) Ans. 6534 v./sec. 

140. Sympathetic Vibration. — Usually resonance is regarded 
as strengthening a sound or bringing it out, but resonance may 
occur without doing this, and a body may be in resonance with 
another in consequence of having a like fundamental period, 
and continue sounding, though perhaps feebly, after the first 
one ceases. Such vibration is called sympathetic vibration. It 
may be shown very readily by depressing a key of a piano, thus 
removing the damper from that string, and then striking the 
key one or two octaves higher. Although the sound from the 
string that is struck is immediately stopped by releasing its key, 
if the other key is held down its string gives out the note of that 
which was struck. 

Experiments Nos. 61 and 62, pages 203 and 204. — Sympathetic vibration. 

141. Selective Absorption. — If a large number of wires were 
strung across a room and tuned to rates of vibration that are 
multiples or submultiples of the pitch of the notes produced 
by an orchestra, a piece of music performed by the orchestra at 
one end of the room would be much weakened, if not wholly 
destroyed, for listeners at the other end of the room, by the ab- 
sorption of the energy of vibration by the wires. Each wire, 
however, would take up only that order of vibration to which it 
was itself tuned. Such a process of taking up energy is called 
" selective absorption." 

142. Corti's Fibers. — In the liquid which fills the internal 
ear are a large number of fibers or . threads that are termini of 
the auditory nerve. These fibers are of various lengths and 
mass and respond to various periodicities of disturbance in the 
liquid. It has been supposed that any vibration of the drum 
of the ear was imparted by the latter to the liquid within, 
and these fibers, selecting the vibrations of their own respective 
periods, furnished at once the stimulus by which the brain per- 
ceives and distinguishes the different sounds, either simple or 
complex. It is now thought that these fibers accomplish only 



VIBRATION OF AIR IN PIPES 



191 



a part, and a minor part at that, of the act of hearing, the sym- 
pathetic vibration really occurring in a so-called basilar mem- 
brane which extends along one of the chambers of the cochlea, 
and upon which rest the Corti 
fibers and also other fibers con- 
nected with the auditory nerve. 
143. Vibration of Air in 
Pipes. — (a) Open Pipes. — In a 
pipe open at both ends, the air 
at each end is free and therefore 
will vibrate as at a loop or ven- 
tral segment. The node nearest 
each end will be at a quarter 
wave length from the end, and if 
the air column breaks up into 
stationary waves it must so 
divide as to have a quarter wave 
length at each end and an inte- 
gral number of half wave lengths 
between them in the pipe. The 
simplest division is with a node in the middle, as at C (Fig. 83 
(a) ; here the length of the pipe is two quarter wave lengths, or 

2 - . The next simplest division is as in (b), in which AC = --, 



\t 



(b) 



(c) 



(a) 

Fig. 83. Division of Vibrating Air 
Column in an Open Pipe. 



2 



EF = -. 

4' 
length /. 



and DE = 



in 



to, AC 



X 
4 
and there are six quarter wave lengths in the total 



CD = DE = -, and 

2 



It is readily seen that the subdivision may be extended, 
but always so as to give an even number of quarter wave lengths. 
That is, the length of the pipe I equals 



X X ^X 

2-, 4-, 6- 

4 4 4 



2 n 



or 



X = 2 1,1, -I, - 1, 



I. 



n 



192 



SOUND 



The rate of vibration of the air column is inversely as the length 
of the wave, or the vibration rates for such a pipe are as the num- 



bers 



n 



— , or as the natural numbers, 1, 2, 3, . . 
2 I 



n. 



2 V 2 V 2 V 

An open pipe, then, will give for its fundamental a tone for 

which X = 2 I, and it is capable of emitting all the harmonics. 

(b) Slopped Pipes. — A resonance column or box closed at 

one end, like those described in 
Art. 139, Resonance, is like an 
organ pipe that is "stopped." 
The stopped end is of necessity 
a nodal point, while the air at 
the open end is free, and that is 
therefore the position of a loop. 
In such a pipe the simplest 
mode of vibration, producing 
the fundamental tone, is when 
the entire length of the tube 



(a) 



equals - , or X = 4 I (Fig. 84a). 
4 



ib) 



(c) 



In any further subdivision of 
the column, since the upper- 
most segment must always be 
a half wave length, and the 
lowermost a quarter wave length, the pipe will contain one, 
three, five, or the odd numbers of quarter wave lengths. That is, 



Fig. 84. Division of Vibrating Air 
Column in a Stopped Pipe. 



X 

I - 

4 



X 
S 4 



and X = 4 /, - /, - /, 

3 5 
and the vibration rates are as 

_L -3_ JL 
4/' \V 4V 



(2» + l)-, 

4 
4/ 



+ 1' 



2 n + 1 



4 i 



that is, as the odd numbers 1, 3, 5, , . . (2 n + 1). Such a 
pipe, therefore, can give out only the odd harmonics besides its 
fundamental. 



VIBRATION OF STRINGS 1 93 

If an open pipe were of the same length as a stopped pipe, its 
fundamental would have a wave length half as great as the fun- 
damental of the stopped pipe, or it would be an octave higher 
in tone. The fundamental of an open pipe whose length is I is 

of the same pitch as that of the stopped pipe whose length is - . 

2 

This may be simply but strikingly illustrated as follows: Select a plain 
open pipe of glass or metal 3 or 4 cm. in diameter and from 30 to 60 cm- 
long. Close one end suddenly with the palm of the hand and as suddenly 
jerk it away. Repeat this rapidly, and a rapid alternation of a note and 
its octave is produced. The lower note is that of the pipe when the hand 
closes it, and the higher when it is opened. 

Since an open pipe is capable of producing all overtones and a 
stopped one only those corresponding to the odd numbers, al- 
though an open pipe of length / and a stopped one of - have the 

2 

same pitch, the sound of the former is richer than that of the 
latter, because it possesses certain overtones which cannot be 
present in the sound of the latter. 

Also illustrate with organ pipes, and exhibit (project) Crova's 
disks: (a) showing fundamental of open pipe; (b) showing second 
overtone of stopped pipe. 

Experiments Nos. 63 and 64, page 204. — Singing flames; resonant pipes. 
Examples. — 

1. What length of closed organ pipe will give a wave 2 meters long? 
What length of open pipe will give the same wave length? 

Ans. 50 cm.; 100 cm. 

2. In the pipes of Ex. 1 what would be the wave length of the first over- 
tone produced by (a) the closed pipe; (b) the open pipe? 

Ans. (a) 66.67 cm.; (b) 100 cm. 

3. If the velocity of sound in air at o° C. is 332 meters per second, what 
change is produced in the note of an open organ pipe 50 cm. long, when 
the temperature rises from io° C. to 35 C? 

Ans. The frequency increases from 338 per second to 353 per second; the 
pitch rises a little less than a semitone. 

144. Vibration of Strings. — Gases can receive or transmit 
only compressural waves, resulting from longitudinal vibration; 
solids may undergo transverse or longitudinal vibration. If the 



194 SOUND 

latter, the waves traversing the solid are sound waves, as they 
were exemplified in Kundt's tube and in Art. 136. With strings 
or wires the vibration is usually transverse, and the sonant effect 
is only obtained by some mounting of the string which will set 
vibrating a sounding board or the cover of a resonance box which 
thus imposes sound vibrations upon the air. A string itself will 
take on rates of vibration of various periods, having a funda- 
mental rate corresponding to its vibration as a whole, and at the 
same time possibly breaking into segments of rates to produce 
overtones. If the string is stretched between two fixed points, 
A and B (Fig. 90; see Experiment No. 65), the distance AB 
is considered the length / of the string. The slowest vibration is 
when the whole string is swinging to and fro, the largest move- 
ment being midway between A and B. The fixed points are 
necessarily nodes, and in this vibration the length of the string 

is half a wave length, or / = -■ Then X = 2 I, and if the string 

2 

is making n vibrations per second, the velocity with which such 
waves travel along the string is n\. An obstacle holding the string 
at its middle point D will cause it to vibrate in two segments, 
or in waves whose length is / instead of 2 /, and by imposing a 
position of rest at proper points, the string can be made to pro- 
duce vibrations of any period for which it can be divided into 
an integral number of segments, i.e., as the successive numbers 
1, 2, 3, ... n. From Art. 120, the rate at which transverse 

IT 
waves travel along a string is given by the equation v = y — > 

where T is the tension of the string and A the mass per unit 
length. If T is dynes, and A is grams per centimeter, v is centi- 
meters per second. Then, since v = n\, 



-vr 



«\ = V~ (A) 

Also if s is the number of segments into which the string divides 

/ 2 1 

itself, - is the length of one segment, and X = — J 



= v/-- 



therefore, £-2i«:\/±.. (B) 

s 



VIBRATION OF STRINGS 195 

If 8 is the density of the material and the string is circular in 
cross-section with radius r, then (i) irr 2 is the volume of unit 
length, and irr 2 8 is the mass per unit length, or the value of A 
in Eq. (B), from which we obtain 

T 



2 It * 



7r5 

For a given value of s, I and 8, n varies as the square root of T, 
and for the fundamental rate s is unity; so the pitch of the string 
varies as the square root of the stretching force. If the string 
is stretched by a weight w a stretching weight of 4 w will produce 
a tone an octave higher, etc. (Compare this with the fact that 
a change of weight makes slight difference in the note if the 
vibrations are longitudinal.) 

With the same material, i.e., 8 being constant, and keeping the 
same value of T while s is unity, doubling the length will halve 
the frequency or lower the tone an octave, and conversely; also, 
with / constant, doubling the radius will halve the frequency. 
All these relations for transverse vibration may be summed up 
as follows: 

With a string vibrating as a whole, the rate of vibration (pitch) is 
proportional, 

(a) Directly to the square root of the stretching force. 

(b) Inversely to the square root of the density. 

(c) Inversely to the radius. 

(d) Inversely to the length. 

These principles all have direct application in stringed instru- 
ments of music. 

Experiment No. 65, page 205. Melde's experiments. 
Examples. — 

1. A string stretched by a weight of 2 kg. vibrates 200 times per second. 
With what weight must it be stretched to give a note an octave higher? 

Ans. 8 kg. 

2. How should the length of the string in Ex. 1 be altered to produce 
the octave when stretched with the 2 kg. weight? 

Ans. It must be one half as long. 

3. The strings of a violin are tuned to G, D, A and E. Suppose the D 



196 SOUND 

string to be of like material and length with the A, but with twice the area of 
cross-section, how does its tension compare with that of A? (Refer to 
Eq. (A), Art. 144, and to intervals of natural scale, Art. 129.) 

Ans. 0.91 1 as great. 

145. Beats; Combination Tones. — If two sounds of equal 
intensity and of like period issue from independent sources so 
situated that at a given point the sounds are in exactly opposite 
phase of vibration, a condensation arriving at the point from one 
source at the instant that a rarefaction arrives there from the 
other, there will be complete interference and no sound will be 
perceived. On the other hand, if the phase of vibration from 
both were the same, both condensation and rarefaction would be 
greater and the sound would be rendered more intense, or be 
reenforced. But if the two sounds differed slightly in period, 
they would agree at one instant and there would then be rein- 
forcement, but gradually the one would gain in phase upon the 
other until it would be a half period in advance ; it would then be 
in opposition, or producing a condensation where the other would 
be causing rarefaction, the two would interfere, and the sound 
would be destroyed ; after a while, however, the faster one would 
gain another half period when they would again reenforce each 
other and a loud sound would result. While the vibrations are 
maintained there will be a succession of loud sounds intermitted 
by silences, or rather a series of alternate crescendos and dimin- 
uendos. These are called " beats." When the two sounds have 
almost exactly the same period (frequency), both the interfer- 
ence and the reenforcement hold for a considerable length of 
time. Two organ pipes thus sounded together, if very slightly 
out of unison, may seem for a considerable time to be not sound- 
ing at all, but with the stopping of either the other will immedi- 
ately be heard. If one sound has one more vibration per 
second than the other, it will gain one vibration per second, and 
there will be one beat (one swelling and one shrinking of sound) 
per second; if the rates differ by two vibrations per second there 
will be two beats per second, and so on. If the difference in 
rate is, say, as great as ten or twelve a second, the beats occur 



MUSICAL INSTRUMENTS 1 97 

as rapid throbs, and their presence gives a roughness or husk- 
iness to the combined sounds. These throbs, however, may 
correspond in period to the rate of vibration of a hall or build- 
ing and set the entire structure to vibrating. When the beats 
are as frequent as twenty or more a second they produce the 
sensation of a separate low tone called a beat tone, or a dif- 
ference tone. Similar effects may be produced by sounding 
simultaneously two notes of very nearly an exact simple ratio, 
as, for example, a note and its octave, and other combination 
tones called summation tones may be produced. 

(The classic on this subject is Helmholtz's Tonempjindungen; 
in the English translation, Sensations of Tone) 

Experiment No. 66, page 206. — Beats produced by tuning forks, also by 
pipes. 

Example. — The rate of vibration of a tuning fork decreases with a rise 
in temperature of the fork. Two forks are in unison, each making 256 
vibrations per second at 20 C. When one is heated to ioo° C, and the two 
are then sounded together, 20 beats are heard in 9 seconds. In what pro- 
portion is the frequency lowered per degree? Ans. 0.000108. 

146. Limits of Audition. — There are from 16,000 to 20,000 
Corti's fibers which unite in a common auditory nerve, but of 
which each is capable of conveying a separate distinct sound to 
the brain. The lowest rate of vibration to which the human 
ear is responsive is given by Preyer as 16, by Helmholtz as 34 per 
second; while the upper limit is given by Despretz as 32,000, and 
by Preyer as 40,000. If we take the inferior limits, i.e., 34 and 
32,000, as more nearly normal, the range of audition is about ten 
octaves. 

(Illustrate with Galton's whistle.) 

147. Musical Instruments. — These are of the utmost variety, 
but they can be arranged in classes, as: 

(a) Wind instruments, in which air columns are set vibrating 
by the edge of a mouthpiece, as in organ pipes, the flute, etc. ; or 
by the lips, as in the cornet ; or by a reed tongue, as in reed organs, 
the clarionet, etc. In all the pitch is varied by means of keys 
except in the trombone and the trumpet. 



198 SOUND 

(b) Stringed instruments, in which the transverse vibrations 
of strings are converted into sound vibrations by a sounding 
board, as in the piano (seventh or ninth node struck out); or by 
a sounding head made of elastic membrane, as in the banjo; or by 
a surface of the instrument constituting one side of a resonance 
chamber in the body of the instrument, as in the violin or guitar, 

(c) Those in which the vibrating surface is directly struck, 
as the membrane of a drum (if that is a musical instrument) or 
the rods of a xylophone. Bells and plates come under this cate- 
gory, while various forms of acoustic apparatus, as the phono- 
graph and the telephone, act by means of a vibrating disk and 
are often used to produce or reproduce music. 

(See, on the subject of this article, Hastings and Beach, General 
Physics, Chapter XXXV.) 



EXPERIMENTS TO ILLUSTRATE CHAPTER IV. 




Experiment No. 51, Art., 123, Sound not transmitted through a Vacuum. 

Under the receiver of an air pump support an electric bell on a felt cushion 
or by an elastic suspension, so as not to communicate its vibrations to the 
plate of the apparatus, and connect through an 
external circuit to the battery. 

As the air is exhausted from the receiver the 
sound of the bell becomes fainter, and when a 
good vacuum is reached it is nearly if not quite 
inaudible. As air is readmitted the sound grows 
louder and regains its full intensity when the air 
as a transmitting medium is completely restored. 

Experiment No. 52, Art. 123. Sound vs. Noise. 

A stick of dry pine wood 15 cm. long, 15 mm. 
thick, and of width equal to or greater than the 
thickness, if dropped upon the lecture table will 
give out momentarily a note of about 780 vibra- 
tions per second (g of the pianoforte scale) . A - 5 ' 
number of such pieces of the same length and width may be tuned by 
varying the thickness, so as to produce the successive notes of the musical 
scale, the thickest being the highest. 

With these laid out in order on the table, a simple air, the notes of which 
lie within the compass of the pieces, may be picked out by simply dropping 
the pieces upon the table. Any one of these notes separately may be 
characterized as sound, but if the pieces are all gathered in the hand and 
let fall together on the table the result is noise. 

Experiment No. 53, Art. 124. Sensitive Flame. 
Heat a piece of glass tubing of \ inch bore, about 3 inches from one end, 
and draw it down to about half its diameter. When cold cut it in two at 
the narrowest place, and soften the narrow end in a flame until the orifice 
is from one and a half to two millimeters in diameter. Connect this nozzle 
to the gas pipe by a rubber tube and clamp it upright above the table. One 
or two inches above it support a piece of wire gauze with about thirty meshes 
to the inch. On turning on the gas at full pressure and lighting it above the 
gauze the flame flares and burns above the gauze noisily with a blue color. 
By turning the gas cock, cut down the pressure gradually. Presently the 
flame will burn steadily, 3 or 4 inches in height, yellow except at the base. 
Now increase the pressure nearly but not quite to the point of making the 

199 



200 



SOUND 



flame flare. It is now sensitive and drops down on the production of any 
noise in its vicinity, responding most readily to the vowel sound ah or the 
pronoun /. The slight variation in pressure at the tip of the nozzle, due to 
the vibrations of the air, is sufficient to break the unstable equilibrium of 
the flame, causing it to burn with the quick rustling that comes with its 
sudden shortening. The flame will dance to a succession of staccato sounds. 

Experiment No. 54, Art. 124. Movement of Sound Waves. 
On a cardboard about 30 cm. in diameter a small central circle has a 
diameter of, say, 2 cm. If a number of points, say 16, are spaced equi- 
distant on the circumference of this circle, and these points are taken in 
succession as centers from which to describe circles, each with a larger 




Crova's Disk. 



radius than the preceding one, a figure is formed having a spiral shaped 
crowded appearance that spreads into an expanded portion. If this disk 
is rotated before a slit, the portions of the curved lines seen through the 
slit will show a travel of condensations and rarefactions from one end of the 
slit to the other, like the progress of sound waves. 

Similar disks may be constructed by proper shifting of centers, so as to 
exhibit various conditions of reflected sound waves. 

When prepared on glass disks of about 12 cm. diameter, they may be 
projected with an ordinary projection lantern. 

Experiment No. 55, Art. 128. Determination of Pitch. 
If a siren disk or a toothed wheel (Fig. 87) is mounted on the axle 
of an electric motor or other rotator, the pitch is easily seen to rise or 
fall with an increase or decrease in the rate at which puffs of air pass 



EXPERIMENTS 



20I 




Fig. 87. Siren, and 
Savart's Wheel. 



through the orifices of the disk, or taps occur on the 
teeth of the wheel against which a card is held 
lightly. 

If the apparatus have a counting device to deter- 
mine its rate of rotation, the actual number of vibra- 
tions per second for any recognized pitch is readily 
determined. 

Experiment No. 56, Art. 134. Manometric Flames. 
A manometric capsule is a small chamber, one part 
of which is separated from the other by a flexible 
membrane as rubber or paper. A tube leads gas into 
one side of this chamber, and the gas passes out 
through a tube that is provided with a fine pinhole 
tip. When the gas is admitted, and lighted at the 
tip, the jet should be reduced to about 3 cm. in 
height. To a tube leading into the other side of 
the chamber is attached a funnel like a speaking 
trumpet. On singing or speaking into this funnel, 

the membrane forming the partition is set vibrating and the resulting 
variations in the pressure upon the gas flowing through the other com- 
partment cause a dancing of the jet of flame. 

A mirror rotated before the flame shows a band of light that is broad and 
even when the jet is undisturbed, but which becomes serrated when a note 
is sounded in the funnel. The serrations are regular or irregular, deep or 
slight, according to the complexity of the sound. 

Experiment No. 57, Art. 134. Production of Overtones. 

If a heavy tuning fork is sounded by drawing a violin bow across one 
prong near the top it emits its fundamental almost exclusively. If over- 
tones are present they are feeble and die out quickly. If the fork is bowed 
near the lower end it can be made to produce an overtone, loud and clear; 
by gently bowing near the top to produce the fundamental, and then bring- 
ing out the overtone, both may be heard together, with the overtone much 
stronger than the fundamental. When the overtone is sounding the vibrat- 
ing prong has a node about one-third or one-fourth of its length from the 
end; this note therefore may be produced by holding the finger against the 
prong at this place and bowing close to the top. 

If the fork is mounted in a horizontal position, with a stylus attached to 
one prong to make a record of the vibrations on smoked glass that is drawn 
along under it when the overtone and fundamental are sounded together, 
the tracing will show plainly the small waves of the former superposed upon 
the longer ones of the latter. 



202 SOUND 

Experiment No. 58, Art. 137. The Kundt's Tube Experiment. 

For comparing the velocity of sound in different media, the experiment 
of Professor Kundt with dust figures is suitable. 

A glass tube (Fig. 88) a meter or more in length and about 2 cm. in diameter, 
is closed at one end by a stopper through which passes a rod of glass or metal 
about a meter long and 4 or 5 mm. in diameter, held at its middle by the stop- 
per or a clamp. The end of the rod within the tube carries a disk of cork which 
fits the tube loosely enough to permit vibration. At the other end of the 

C A B 



f *•■*» * tfi^a 




Fig. 8&. Kundt's Tube. 

tube is a plunger that can be moved into the tube or withdrawn, over a 
range of 15 or 20 cm. Scatter within the part AB of the tube a small 
quantity of cork dust or lycopodium powder; stroke the portion CD of the 
rod with a piece of rosined chamois skin so as to produce a clear sound. 
The disk A vibrates with the longitudinal vibration of the rod and sets up 
vibration of the air in AB. If AB is of a suitable length to divide into seg- 
ments of stationary waves, it will so divide, and immediately the powder will 
gather into spindle-shaped segments, indicating nodes and loops, each such 
segment being a half wave length in the air, for the note emitted by the rod. 

If on stroking the rod the dust is not thus disturbed, move the plunger 
B in or out as the rod is sounded until this result is attained. The rod itself 
is a half wave length in the metal for its rate of vibration; therefore the 
velocity of sound in the rod and in the air is as the wave lengths, or as the 
half wave lengths, i.e., as the length of the rod compared to the length of 
one segment of the air column. By measuring the distance in the tube 
occupied by several segments a tolerably correct average is obtained. 

With rods of different materials, the velocity in each can be compared to 
that in air, and hence to that in any of the other rods. Also, if one rod is sound- 
ed in air, and then the tube is filled with some other gas, as illuminating gas, 
and the same rod is sounded in it, the velocity of sound in the two gases may 
be at once derived by the ratio of the segments or half wave lengths in them. 

Further extension of the experiment is discussed in advanced acoustics. 
See Barton's Text-Book of Sound (The Macmillan Company). 

Experiment No. 59, Arts. 138 and 139. Resonance. 
To the lower end of a tube 3 or 4 cm. in diameter and about a meter in 
length, attach an outlet pipe with a stopcock. Starting with the tube 
nearly full of water, hold above it a vibrating tuning fork as in Fig. 82, 
Art. 139, and, opening the stopcock, let the water sink slowly. Mark the 
level at which the first strong resonance occurs. The air column in the tube 
above this level is the resonance column; the water has nothing to do with 



EXPERIMENTS 



203 



the experiment except to afford an easy means of varying the length of the 
air column. To the length of the latter, at the first resonance, add about 
0.8 times the radius of the tube; the sum makes one quarter- wave-length in 
air for the frequency of the fork used. This quarter- wave-length multiplied 
by 4, and that by the number of waves per second made by the fork, gives 
the velocity of sound in air at the temperature in the tube. 

Continuing to let the water escape, resonance occurs again at a lower level, 
where the air column plus 0.8 times the radius of the tube equals three quar- 
ter-wave-lengths, from which again the velocity of sound may be computed. 

A tube a meter in length will give both the first and second resonances 
for a fork whose frequency is 256 or higher; for one of 430 vibrations per 
second it will give a third resonance length. 

Instead of using an efflux tube, a tall narrow jar of water may be used, 
into which the resonance tube dips to just such depth as makes the air column 
in it above the water to resound. With this arrangement a metal tube can 
be used instead of glass, for the height of the resonance column can be 
measured as well on the outside of the tube as on the inside. 

Note. — The correction on account of width of the tube is slight, and in a demon- 
stration may be neglected. It varies with the size of the tube, from 0.8484 R for 
a narrow tube to 0.7854 R for a wide tube. It is due to the fact that the wave front 
at the open end of the tube is convex outward. 

Experiment No. 60, Arts. 138 and ijq. 
Rotate a vibrating tuning fork before the open end of its resonance box, 
or over the top of the air column that resounds to it, as in Fig. 89. For four 
positions in one rotation silence 
results from interference. While 
the fork is held in one of these 
positions, carefully slip a cylinder 
of paper or cardboard over one 
prong without touching the other. 
The pipe or box resounds to the 
vibration of the exposed prong; 
on removing the cylinder inter- 
ference again causes silence. 

Experiment No. 61, Art. 140. 
(Nos. 61 and 62 illustrate Sym- 
pathetic Vibration.) 
Stretch a heavy cord, 8 or 10 
meters in length, across the room, and about 2 meters from each end 
suspend a pendulum of about 2 meters in length, both having the same 
period of oscillation. Set one pendulum swinging; the other takes up the 
motion and is soon swinging in unison with the first. 




Fig. 89. 





Interference of Sound. 



204 SOUND 

A similar effect is produced if the two swinging bodies are bobs suspended 
from helical springs and oscillating vertically in the same period. The 
latter arrangement will work if the weights are suspended from two points 
of a flexible lath supported at its ends on the backs of two chairs. 

Experiment No. 62, Art. 140. 
If two tuning forks are exactly in unison, either will set the other vibrat- 
ing. Place their resonance boxes facing each other at a distance of one or 
two meters apart; sound one fork and after a few seconds stop its vibrations 
with the finger. The other fork will be sounding. 

Experiment No. 63, Art. 143. Singing Flame. 

When the flame is adjusted to sensitiveness in Experiment No. S3, hold 
vertically above the flame, and resting on the wire gauze, a tube 25 to 30 mm. 
in diameter and 40 to 50 cm. in length. The flame will probably flutter 
and the pipe will emit a loud clear sustained note. If it does not at once do 
this, raise the gauze and tube together carefully a little higher over the gas 
nozzle; a position will presently be reached at which the flame will flutter 
and the pipe will sing. A metal tube is preferable, as a glass one is apt to 
break. 

Support in a vertical position a tin pipe about 3 inches in diameter and 
4 or 5 feet long (a piece of ordinary rain pipe will answer) ; attach a rose gas 
burner to a half-inch gas pipe, and that, by a rubber tube, to the gas cock at 
the lecture table. When the burner is lighted, insert it in the lower end of 
the pipe and gradually raise it. At the distance of 10 or 15 cm. from the 
lower end, it produces a deep roaring sound in the pipe. 

Experiment No. 64, Art. 143. Resonance Pipe. 

Use the siren disk of Experiment No. 55, Art. 128, and a tube of glass or 
metal 3 or 4 cm. in diameter and, say, 80 cm. long, open at both ends. 

Support the tube perpendicularly to the plane of the disk and close to it 
on the opposite side from the nozzle giving the jet of air. With air blowing 
through the nozzle, when the disk reaches a sufficient speed the tube will 
resound. At the temperature of 20 C, with a tube of the above dimensions, 
the first resonance will occur when the siren is producing about 210 puffs per 
second. There is then a node in the middle of the tube, and the length of 
the tube is half a wave length. A second resonance will occur with double 
the speed of the disk and again when the first speed is trebled, and so on. 

If the same pipe have the end farthest from the disk stopped, it will 
resound first at about 105 vibrations per second, for which the length of the 
pipe is one quarter- wave-length; next at three times this speed; then at 
five times, and so on. Other sizes of pipe may be used to vary the experi- 
ment. (See Ames and Bliss' ; Manual of Experiments in Physics, Exp. 43.) 



EXPERIMENTS 



205 



Experiment No. 65, Art. 144. Melde's Experiments. 

Attach one end of a light braided string AB, about a meter in length, to 
a prong of a tuning fork (a fork that is driven electrically is preferable if 
available), carry the string over a light pulley B and hang a weight W at 
the end. If B moves freely W is the tension in the cord AB. Set the fork 
vibrating and adjust the weight until the string gives the appearance of two 
spindles, as ADB. It is then vibrating as a whole in unison with the fork. 




u 



w\ 

Fig. 90. Transverse Vibration of Strings, by Melde's Experiments. 

In one complete vibration of the fork a disturbance travels along the string a 
distance of one wave length, creating the form of the heavy line ADB; if this 
is reflected from B it gives the light line BDA. If W is made one fourth 
as great the string will vibrate in four segments or two wave lengths. The 
wave now travels from A to B in two vibrations of the fork, or it requires 
twice as long to set the entire string vibrating as before; i.e., the number of 
vibrations of the string in a given time is only one half as great if the weight 
is one fourth as much as at first; if W is reduced to one ninth of its first value, 
there will be six spindles, or the string will make one third of a vibration in 
the period of the fork, and so on, the rate of vibration of the string varying 
as the square root of the tension. 

With a given cord, if a certain length and tension give a certain number 
of segments, twice the length of string with same tension will give twice as 
many segments (i.e., half as frequent vibration of the whole string), three 
times the length of string will give three times as many segments, or one 
third as many vibrations of the string, and so on, the rate of vibration of 
the string being inversely proportional to the length. 

Again, if a vibration with a definite number of segments be obtained for 
a length / of thin cord or fine wire with a definite tension T and definite mass 
per unit length, then with another cord of the same length and tension, but 
with a mass per unit length four times as great, it will vibrate just half as 
fast, i.e., give double the number of segments, and a cord of nine times the 
mass per unit length will vibrate one third as fast, or show three times as 
many segments, and so on, showing that the rate of vibration of the cord is 



206 SOUND 

inversely as the square root of the mass per unit length. This is illustrated 
by beginning with a light cord of single strand, then using four strands of 
same length and material, then nine. 

For the case where the motion of the fork is in the direction of the length 
of the string instead of transverse to it, see more advanced works on Physics 
or Acoustics. 

Experiment No. 66, Art. 145. Beats. 

Sound two forks that have the same frequency. Place a little wax on 
the prong of one fork, thus reducing its rate of vibration. When both forks 
are sounding, now, there will be a slow alternation of swelling and diminish- 
ing sound; on adding more wax, these alternations become more rapid. 

Two pipes in unison may be made to produce beats by partially cover- 
ing the open end of either one. 

A conductor's whistle is often made of two small pipes of slightly different 
pitch. When sounded together they give beats so rapid as to produce a 
tremolo, as if a ball or some obstruction in the pipe had caused the interrup- 
tions in the sound. 



CHAPTER V. 
POTENTIAL; MAGNETISM; ELECTRICITY. 

148. Theory of Potential. — Under the general terms Poten- 
tial and Field of Force are to be developed several special 
ideas underlying the study of energy as it is manifested in the 
various branches of Physics. The presentation of elementary 
principles in the following eight articles is adapted in large part 
from Cumming's Theory of Electricity. 

149. Field of Force. — Near any material system, if we try 
to move a mass of matter from one position to another, the move- 
ment is either resisted and work has to be done in moving the 
mass, or if we move it in the opposite direction a force assists the 
movement and would, if the mass were free to obey the force 
without friction, generate in it kinetic energy or do work on it 
during the fall. To express this condition in any space the term 
" Field of Force" is used. Defined thus: Field of force is any 
bounded or unbounded region in which any two points A, B 
being taken, work has to be done to move a mass from A to B, 
while kinetic energy is generated if the mass be allowed to fall 
without friction from B to A . 

In either case the numerical measure of the result is the same. 
The field of force is specially characterized by the form of energy 
in consequence of whose manifestation the field of force exists; 
for example, it may be gravitational, thermal, magnetic or elec- 
trical, in which the amounts of work or kinetic energy indicating 
the fields of force will depend upon different relations ; but there 
are several fundamental conceptions which are general and 
which apply alike to fields of force whatever may be the form 
of energy concerned. 

150. Line of Force. — At any point in a field of force there 
is a definite direction of the resultant force at that point, along 
which a mass of matter left to itself will tend to fall. By 

207 



208 POTENTIAL; MAGNETISM; ELECTRICITY 

choosing points near enough together, such that the line joining 
each two consecutive points shows the direction of the resultant 
force at a point on that line, we shall have a broken line through 
the field so that its direction at every point shows the direction of 
the resultant force near that point. If the points be taken close 
enough together this broken line becomes a continuous curve, 
such that the tangent at every point shows the direction of the 
resultant force at that point. This curved line is then a line of 
force; hence the definition: Line of force is a line in a field of 
force such that the tangent to the line at any point shows the 
direction of the resultant force in the field at that point. 

One line of force passes through every point in the field, and 
lines of force cannot intersect at any point where there is 
one resultant force, for if they could there would be at the 
point of intersection more than one direction of the resultant 
force. 

151. Strength of Field. — The magnitude of the force by 
which a mass of matter is urged along a line of force depends 
jointly on the held or system of force and on the quantity of 
matter. To compare force at different points in the field, we 
should place at those points a unit of mass and find the force it 
experiences. In the c.g.s. system the unit of mass is the matter 
in one gram. 

Strength of field at a point is the magnitude of the force (num- 
ber of units of force) experienced by & unit of mass when placed 
at that point in the field of force. If the systems of bodies and 
forces are of the kind to which Newton's laws of motion apply, 
the strength of field is clearly the force per unit mass, and this 
is numerically equal to the acceleration which a body would 
acquire in the field, since Force = Mass X Acceleration. Thus 
the strength of the earth's gravitational field at the surface of 
the earth is 980 dynes, since a gram experiences 980 units of 
force as it undergoes an acceleration of 980 cm. /sec. 2 (see Art. 28). 
When we know at every point in a field of force the strength of 
field and the direction of the fine of force, our knowledge of that 
field of force is complete. 



DIFFERENCE OF POTENTIAL 209 

152. Potential. — Our study is simplified if we can express 
both the direction of the line of force and the strength of field in 
terms of one quantity. The name given to the quantity ex- 
pressing the condition of a field of force in these two respects is 
''potential," and potential is studied by comparison, referring 
to some arbitrary level for zero, or by directly examining differ- 
ence of potential at any two points. This is somewhat analogous 
to observing the difference of temperature between two bodies 
without regard to the absolute temperature or the actual amount 
of heat of either body. 

By the potential at a point is to be understood the amount of 
work that would have to be done to bring a unit body (unit mass 
if the force is gravitational) from an infinite distance, or from 
without the field of force, to this point, against the forces of the 
field. 

153. Difference of Potential. — If any two points, A, B 
(Fig. 91), be taken in a field of force, and a unit of matter be 
carried from A to B against the force in the field, a certain 
amount of work will be done on the 
unit, and if the unit of mass be allowed 
to pass back from B to A by friction- 
less constraint, the particle will acquire 
an equal amount of energy in its fall. 
The principle of the Conservation of 
Energy shows that the amounts of Fl &- 9I - 

work or energy will be the same, whatever path be pursued 
from A to B or from B to A, respectively; for if more energy 
were acquired in falling along a path BCA than along another 
path BDA, then by allowing the particle constantly to fall 
along BCA, and to return along ADB, we should have unlim- 
ited source of energy. 

The distribution of energy in a field of force is for the most 
part studied by examining not the absolute potential at any 
point, but the difference of potential between two points. 

Difference of potential at any two points is the work done in 
carrying a unit of mass from one point to the other, and is 




210 POTENTIAL; MAGNETISM; ELECTRICITY 

independent of the path traversed, depending only on the posi- 
tion of the two points in the field. 

Zero potential is the potential at a certain point chosen as a 
standard of reference; any point which requires work to be done 
to bring the unit of mass from the zero point to it will have 
positive potential, and any place which requires work to be done 
to bring the unit of mass from it to the zero point will have 
negative potential. 

Let A and B be two points in a field of force, and let F be the 
average force along AB. Let V be the difference of potential 

between A and B, then V = F X AB, or F = -~. But if 7 

AB 

V 

is the total difference of potential between A and B, then—— 

AB 

expresses the space rate of change (i.e., change per unit of dis- 
tance) in potential from A to B. Hence the average force along 
any line is given by the average rate at which the potential 
changes along the line, and if the line be made very short we may 
say that the force at a given point in a given direction is the rate 
of change of potential at that point. and in that direction. Since 
the resultant force at a point is in the direction of the line of force, 
the force along any direction at an angle with the line of force 
less than a right angle will be less than the resultant force: it 
follows that the potential changes most rapidly along the line of 
force, and less and less rapidly in directions more and more in- 
clined to the line of force, while in a direction at right angles to 
the line of force the rate of change of potential must vanish. 

154. Equipotential Surface. — If, then, a surface be drawn 
through the field of force which everywhere cuts at right angles 
lines of force, the rate of change of potential along such sur- 
face will be zero, or the surface will be an equipotential surface, 
and the force resolved along it will always vanish, so that no 
work is done in moving matter along such a surface. Due to 
the earth's gravitation, the surface of the sea is an equipotential 
surface, and so far as the effect of gravity is concerned no work 
is required to move a body along the surface of water. 



MEASURE OF THE POTENTIAL AT A POINT 211 

An equipotential surface, then, is a surface drawn through all 
points in the field at which the potential is the same; it will 
everywhere cut lines of force at right angles. 

155. Measure of the Potential at a Point. — The actual work 
involved in transferring a body from one point of a field of 
force to another, or to bring a body to a given point in the 
field, will depend upon the law of force that exists between 
the bodies or things concerned, and in consequence of which the 
field of force exists. In a gravitational field the force between 
bodies is directly proportional to the product of their masses 
and inversely proportional to the square of the distance between 
them, and a similar law holds in connection with magnetism and 
with electricity. This law, therefore, is the one we are to take 
into consideration. 

The mass upon which work is to be done in transferring it is 
unity, and if a mass m is at a point O (Fig. 92), the potential 
due to m, at any point 
whose distance from 

is r, equals — • Without 

the calculus this may 
be demonstrated as 
follows (see Cumming's 
Theory of Electricity, 
Art. 39, Chapter II, 
Theory of Potential). 
"To find the work 

, . . Fig. 02. Difference of Potential between 

done in carrying a gram Two points 

against the attraction" 

(or repulsion) "of any system of particles from one point 

to any other point, or to find the difference of potential between 

two given points." The mass m is at 0, B and A are two given 

points, and PQ is a very small element of the path from B to A . 

Draw QN perpendicular to OP. The mean attraction (or re- 

7ft 

pulsion) on a gram between P and Q is , . , a mean pro- 




212 POTENTIAL; MAGNETISM; ELECTRICITY 

portional (not arithmetical mean) between — — and — - . This 

(fft \ fyi PN 

OP.qq ) cos 0P & or OP-OQ X PQ ' 
and the work of carrying the gram from P to Q is 

m RN = m-PN = tn(OP - OQ) 

OP- OQ' PQ* ^~ OP.OQ~ OP-OQ 

= m (dQ-cb} 

Similarly, the work to carry the gram from Q to R is 
and from R to 6* it is 



\OS 



-m 



so that from P to S it is 
m 



\\OQ Op)^\OR OQ/ + \OS OR/i 

and so from B to A it is 

If there are other masses m h m 2 , etc., at points O h 2 , etc., a 
similar expression represents the work of transferring the unit 
mass for each of these, and the total work to take a gram 

from P to Q is 5} m ( — — — — - ) and between B and A it is 
^L \OQ OP J A 



^[ m {k- 



OQ 
which is independent of the path between 



i 
OB, 

B and A. This is the potential difference between A and B. 

If B is at ah infinite distance, — — is zero, and zJI^ttt) De ~ 

OB ^\ OAl 



comes 
at B. 



the potential at A. Similarly, 2) ( w ^j * s tne potential 



APPLICATION OF POTENTIAL TO MAGNETISM 213 

A neater and simpler demonstration is afforded by the calculus. 
Let q be the quantity at (whether matter, electricity or magnetism), 
and r the distance from to the unit quantity that is to be transferred. 

Then the force upon the unit quantity is * ; at P, F = —^ , in the direc- 
tion OP; the component along the path of motion is F multiplied by the 
cos. of the angle which r makes with the path at the given point; i.e., 

ClY CI (IV 

F X — > or «t- The element of work performed in carrying the unit 
as r 2 as 

through the distance ds is 

dw= <L4f ds = q J? 
r 2 as r L 

The difference of potential between A and B is the work of carrying the 
unit from B to A and is the integral of dW between the limits r = OB and 
r = OA. Designating potential by V we have 

and is independent of the path. If B is at an infinite distance from O then 
~- is the potential at A due to q at O; or, in general, 

r 

156. Application of Potential to Magnetism. — The defini- 
tions and propositions thus far presented concerning potential 
and fields of force are applicable to any system of bodies to 
which Newton's laws of motion are applicable and in which the 
law of force is that of the inverse square of the distance. We 
may proceed to apply them to fields of magnetic force and see 
what the definitions become and what the principles indicate. 

Phenomena. — A magnet attracts iron. Like poles of magnets 
repel and unlike attract each other. Try two magnets upon a 
third which is pivoted or suspended, to find which are "like 
poles," then verify the statement by trying these two upon each 
other. Usually poles are marked N. and S. and the magnetism 
of N. is + and that of S. is — ; N. is used for the pole which, if 
the magnet were suspended, would point to the north. In France 
it is customary to call this pole the south pole, S., and in England 
and America it is not unusual to call it the north-seeking pole. 



214 POTENTIAL; MAGNETISM; ELECTRICITY 

The strength of a pole can be expressed by the force which it 
exerts upon another pole, and the unit in terms of which it can 
be measured is defined thus: 

A unit magnetic pole is a pole which exerts upon an equal pole 
unit force at unit distance. In c.g.s. units this is a force of one 
dyne at a distance of one centimeter. 

Moment of a magnet is the product of the strength of either 
pole by the distance between the poles. 

Force between Two Poles. — The force of attraction or repul- 
sion between two magnetic poles is directly proportional to the 
product of the strengths of the poles and inversely proportional 
to the square of the distance between them. This law is deduced 
from experiment. With the above definition of unit pole, calling 
the strength of two poles m and m' ', and the distance between 

mm 

them r, the expression for the force becomes force = . This 

r 2 

force is repulsive if the numerator is plus and attractive if 

minus. 

Under the influence of magnetic poles, then, a field of magnetic 
force exists whose general laws are identical with those of gravi- 
tational force. The only change required is to read "unit pole," 
or particle charged with unit of positive magnetism, in place of 
the unit of mass there employed to test the field. So our pre- 
vious definitions will read: 

Field of magnetic force is the region surrounding magnetized 
bodies, within which work has to be done to move a magnetic 
pole. 

Lines of force are lines in the field such that the tangent at 
each point shows the direction in which a magnetic pole placed 
there would be urged. 

Strength of field at a point, or magnetic force at a point, is 
the force with which a unit magnetic pole would be urged if 
placed at that point. 

Magnetic potential at a point is the work which would be done 
in bringing a unit magnetic pole to that point from an infinite dis- 
tance or from a point outside the field of force. If there be a dis- 



MAGNETIC POTENTIAL 



215 



tribution of magnetism consisting of quantities m h m 2 , . . . m n 
at distances r h r 2 , . • . r n from the given point, the measure of 
the magnetic potential at the point will be 

Mi 



+^+ 



m n 



or 



s(") 



Examples. — 

i. " Find the magnetic potential due to a bar magnet 10 cm. long, and 
of strength 80, at a point P, lying in a line with the magnet poles and 6 cm. 
distant from its north-seeking end." 

- 80 +8 6 cms. P 

S 



10 cm. 
Potential at P = 



N 



■33- 



2. " A N.-seeking and a S. -seeking pole, whose strengths are respectively 
+ 120 and —60, are in a plane at a distance of 6 cm. apart. Find the point 
between them where the potential 
is o, and through this point draw the 
curve of zero potential in the plane." 

In Fig. 93, let the poles N and 
S be at A and B respectively. 
AB = 6 cm. Let C be the point 
where the potential equals zero. 
Then 

120 _ ^o _ t 120 _ 60 

AC ~ BC~°'' ° r AC ~ 6 - AC 
Whence AC = 4 and BC = 2. 

For the locus of the point P so that its potential shall everywhere be o, 
taking origin at A, and axes X and Y as in the figure, at every position of 
120 60 




Fig. 93- 



P we must have 



or 



AP BP' 



60 



v*2 4- 3,2 V(6 - x) 2 + y 2 



whence x 2 — 16 x + y 2 = — 48, the equation of a circle. For the points 



where it cuts the axis of X, y = o, and x 
and D; therefore BD = 6. 

If the origin be transferred to 0, midway between C and D, make x 
and y = y', and substitute in Eq. of locus; it becomes 

x' 2 -\- y' 2 = 16, a circle whose center is at and whose radius is 4. 



4 or 12, locating the points C 
*'+8 



2l6 POTENTIAL; MAGNETISM; ELECTRICITY 

Experiment No. 67, page 296. — Exhibit lantern slide illustrations of 
magnetic lines of force; also form and project the lines. 

Experiment No. 68, page 296. — To show that the force between two 
given poles varies inversely as the square of the distance between them. 

Examples. — 

1. A magnetic pole of strength 22 is placed in a magnetic field of strength 
0.68. What is the force experienced by this pole? Ans. 14.96 dynes. 

2. What is the strength of a magnetic pole that is urged with a force of 
150 dynes when placed in a magnetic field whose is intensity is 2.5? 

Ans. 60 c.g.s. units. 

3. A and B are successive corners of a regular hexagon whose sides are 
50 cm. in length. A has potential +60, and B, —40, required the work 
to move q units from B to A by the shortest path, and also by going along 
the perimeter of the hexagon. (See Art. 1 53.) Ans. 100 q in either case. 

4. A magnetic pole of 140 units' strength is placed at a distance of 15 cm. 
from a like pole of 30 units' strength. What is the force between them? 

Ans. A repulsion of 18.67 dynes. 

5. A plus pole of 60 units' strength is placed 5 cm. from a minus pole of 
172 units' strength. What force is exerted upon the latter by the former? 
What upon the former by the latter? 

Ans. An attraction of 412.8 dynes. 

157. Physical Interpretation of Lines- of Force. — Lines of 
force being denned, as above, by direction simply, and strength 
of field at any point being denned with reference to the force 
upon a unit pole at that point, the character of the field can be 
understood and treated mathematically; but Faraday combined 
the idea of direction and magnitude of force in one, by giving to 
lines of force a physical meaning as if they were actual strings 
stretched to a definite pull of unit force (in c.g.s. units a force of 
one dyne) and distributed throughout the field in such number 
as to represent the strength of the field. In a uniform field these 
lines are distributed uniformly, and in field of varying strength 
they are packed closely at some places and sparsely at others. 
In a uniform field of unit strength there is one line per square 
centimeter of area perpendicular to the line; in a uniform field 
of ten units' strength there are ten of these dyne lines piercing 
every square centimeter, and more of these lines can be called 
into being or put out by any agency of a nature that can vary 
the strength of a magnetic field. 



MAGNETIZATION BY INDUCTION 217 

This mode of depicting a field of force is useful and is applied 
not only to magnetic but also to electric fields of force, and is 
further elaborated by the idea of " tubes of force " comprising 
within them groups of lines, the tubes themselves occupying the 
entire field instead of leaving gaps as is necessarily done when 
only the lines are thought of (see infra, Art. 168). 

158. Magnetic Substances. — There are bodies which ordi- 
narily are not magnets but which, under certain influences, may 
become such, and which may again lose or be deprived of their 
magnetic character. Substances of which such bodies consist are 
called magnetic substances. The chief are iron, steel and nickel. 

159. Magnetization by Induction. — The simplest way to 
magnetize a body is to place it in contact or to stroke it with 
a magnet, but this is not the way in which bodies are usually 
magnetized. Magnetic substances are always magnetized when 
brought into a magnetic field, without being in contact with any 
other bodies, and they are then said to be magnetized by induction, 
the extent to which they are magnetized depending upon some 
molecular quality of their own and upon the strength of the field. 
A body thus magnetized is called a temporary magnet if it loses 
its magnetism when removed from the field; a permanent, if it 
retains its magnetism. Soft iron makes a temporary magnet, 
hard steel a permanent one. Various magnetic fields may be 
produced by various arrangements of magnets, and may be 
partially exhibited by means of iron filings. 

The extent to which magnetic substances are affected by 
magnetic fields of force, and the relation of strength of field to 
magnetization produced are known by technical terms such as 
susceptibility, permeability, intensity of magnetization, induc- 
tion, etc., the consideration of which is deferred until we come 
to consider magnets and magnetic fields of force produced by 
electric currents. The direction of a line of force being the di- 
rection in which a N.-seeking pole would be urged, the lines are 
regarded as pointing out from the N. pole of a magnet, and into 
the S. end. A piece of iron, then, placed in the vicinity of a 
magnet, will have a S. pole induced nearest the N. end of the 



?i8 



POTENTIAL; MAGNETISM; ELECTRICITY 



magnet and a N. pole farthest from the N. end of the inducing 
magnet, and if placed in any magnetic field the direction from 
its S. to its N. pole will be that of the lines of force in the part 
of the field in which the iron is placed. 

The directive action everywhere exerted upon a magnetic 
needle shows that there is a magnetic field about the earth, called 
the earth's magnetic field, and an iron bar becomes magnetized 
by virtue of its mere presence in this field. If placed in a north 
and south direction the end towards the north acquires N. -seek- 
ing polarity, the other, S. -seeking. The lines of force in the 
earth's field, however, are not horizontal but incline downward 
at an angle with the horizontal known as the inclination or dip 
of the needle. 

Experiment No. 6g, page 296. — Magnetization by induction in earth's 
field; measure inclination. 

Example, p. 904, Watson's Physics. 

"A magnet is placed horizontally in the magnetic meridian due south of 
a compass needle. How will its action on the latter be affected if (1) a plate 

of soft iron is interposed 
between the two? (2) a 
rod of soft iron is placed 
along the line which joins 
their centers?" 

In Fig. 94 (1), ns is the 
needle, and it is seen that 
if the plate P is absent 5 
is repelled by the magnet 
M. When the thin plate 
P is interposed M induces 
polarity in P, but the 
two faces n', s' are so 
near each other that the 
effect of either upon .? is counteracted by the other, so that the plate 
shields ns from M. In (2) M induces + and — poles n' and s' in the bar, 
but they are so far apart that s' exerts a strong repulsion upon s, and ns is 
deflected more than by M alone. 

160. Terrestrial Magnetism. — Besides the inclination or dip 
which we have just considered, there are other elements con- 
nected with the magnetic field of the earth, as declination, or, as 




STATIC ELECTRICITY 219 

it is sometimes called, variation of the compass, and the changes 
which take place in these angular positions of the magnetic needle 
as well as the actual strength of field. (See Watson, Arts. 432, 
434. For theory of the earth's magnetism, see Barker, p. 605, 
and Hastings and Beach, Art. 325.) 

Electricity. 

161. Static Electricity; Electrification; Ether Stress. — Sum- 
marize elementary ideas. Friction between any two heteroge- 
neous substances puts the bodies into two opposite states or 
conditions called electrification. When a body is in this particu- 
lar condition it is said to be charged with electricity or to con- 
tain electricity. Always two electrifications are produced, equal 
in amount. The electrifications are of an opposite character 
and tend to neutralize each other upon a conductor, i.e., a body 
which permits such readjustment; but a body which does not 
so permit adjustment upon it is a nonconductor, and a sub- 
stance of such material, when separating two conductors, is 
called a "dielectric." 

The fundamental phenomena of electricity are attraction and 
repulsion. 

Electrification is either of the sort produced upon glass by 
rubbing it with silk, and is called vitreous or positive, or it is of 
the sort produced upon sealing wax or hard rubber by rubbing 
it with fur or wool, and is called resinous or negative. In these 
cases, the silk becomes negatively electrified and the fur posi- 
tively. Each is a nonconductor, and so is dry air, and if the 
silk and the glass thus electrified are suspended each by a silk cord 
and separated by air or any other dielectric, they will attract 
each other by some action transmitted through the dielectric. 
The action of an electric charge through a dielectric varies with 
different media, and so the seat of the action is thought to be the 
ether itself, its facility of action being determined by its associa- 
tion with one form or another of gross matter. 

Bodies similarly electrified repel one another, those of unlike 
electrification attract. When such attraction or repulsion exists 



2 20 POTENTIAL; MAGNETISM; ELECTRICITY 

between two bodies not in contact, the ether transmitting the 
force is said to sustain a stress and to be itself strained, like the 
spring between the bodies A and B in Fig. i, Art. 16. The effect 
of this strain is felt by the material occupying the space be- 
tween the bodies, and may be severe enough to shatter the 
dielectric. 

But a body electrified either positively or negatively will at- 
tract to it light bodies that are apparently unelectrified, as will 
be explained under Electrification by Induction. 

Illustrations. — Paper cylinder rolled along table by electrified sealing 
wax; pieces of thin paper drawn between sleeve and waist of the coat will 
adhere to the wall, etc. 

As the electrification of a body may proceed to a greater or 
smaller extent it is said to be charged with a greater or smaller 
quantity of electricity. 

Unit quantity of electricity is such a quantity as will repel an 
equal quantity of the same kind at a unit distance in air with a 
unit force; in c.g.s. units, at a distance of one centimeter with 
a force of one dyne. 

The law of force with electric charges is similar to that of mag- 
netism and of gravity, viz. : Force is proportional to the product 
of the quantities and inversely proportional to the square of the 
distance, so that with the above definition of unit quantity, 

d 2 

162. Electric Field of Force; Electric Potential. — An electric 
field of force is a region in which work has to be done to move a 
quantity of electricity from one point to another. The electric 
difference of potential between two points is the work that must 
be done to transfer a unit of electricity from one of the two points 
to the other, and the potential at a point is the work that would 
have to be done in bringing a unit of positive electricity to that 
point from an infinite distance or from a point without, the field 
of force. There may be a potential at a point whether there is 
a body there or not, and whether there is electricity there or not. 



CAPACITY FOR ELECTRICITY 221 

Since the law of force is like that for magnetism, the expression 
for the potential at a point at a distance r from a quantity q is ?, 
and for that due to various quantities at various distances is 

For instance, if charges of 12, 40 and 20 units be placed at 
the corners A, B, C, of a square A BCD whose side is 50 cm., to 
calculate the value of the potential V at the point D. 

F = ^ + _4^ + 22 =I . 2 . 

5° 50V2 5° 

Similarly at E, the intersection of the diagonals, the potential 
V' = 2.04. The difference of potential between E and D is 2.04 
— 1.2, or 0.84 erg, and this is the amount of work that would 
be required to carry a unit of positive electricity from D to E. 

Examples. — 

1. Two small bodies are charged respectively with 50 and 75 units of 
positive electricity. What is the force between them when they are 20 cm. 
apart? Ans. 9.375 dynes, repulsion. 

2. If a body having 200 units of positive charge of electricity is attracted 
by another charged body with a force of 50 dynes at a distance of 16 cm., 
what is the charge upon the second body? Ans. 64 units, negative. 

3. How much work is required to carry a charge of 250 units of electricity 
(a) from a place where the potential is 30 to another where it is 80, (b) from 
a place where it is — 60 to another where it is + 200? 

Ans. (a) 12,500 ergs; (b) 65,000 ergs. 

4. Charges of 5 units of electricity are placed at each of the four corners 
of a square whose side is 12 cm. What is the electric potential at the point 
of intersection of the diagonals? Ans. 2.353. 

163. Capacity for Electricity. — The potential of the earth is 
usually assumed arbitrarily as zero. Upon a conductor elec- 
tricity passes from a point of high to a point of low potential, or 
distributes itself until the conductor is everywhere at the same 
potential. A body put to earth comes at once to zero potential, 
or loses its charge by sharing it with the whole earth. An 



222 POTENTIAL; MAGNETISM; ELECTRICITY 

insulated conductor rises in potential with an increase of charge, 
the amount needed to raise its potential by any definite amount 
depending on the shape and size of the body and its situation 
relatively to other charges of electricity. By the electrical ca- 
pacity of a body is meant the quantity of electricity required 
to change its potential by one unit. (Compare with capacity 
for heat.) 

164. Electrification by Induction. — If AB (Fig. 95) is an in- 
sulated conductor and C a body charged with, say, positive elec- 
tricity, the conductor AB is found to be charged negatively at 
the end next the positively charged body C and positively at the 

farther end, as if the + charge 
on C had attracted a — charge 
to A and repelled a correspond- 
ing + charge to B. With a given 
quantity on C, and at a certain 
position of C, this separation on 
AB is only carried to such an 
extent as to bring the whole con- 
ductor AB to the same poten- 

Fig. 95. Induced Electrification. . r 

tial, but the + charge is repelled 
to the utmost limit of AB and only stops at B because that is 
the end of the conductor. If B be connected to the earth by 
simply touching B with the finger, AB becomes continuous with 
the earth and the so-called free + electricity is discharged to 
the earth while the minus remains bound at A by the presence of 
C. If now, after breaking connection with the earth, C and AB 
be separated from each other a considerable distance, the minus 
charge will distribute itself over the whole of AB and this body 
is then said to be charged by induction, or the charge upon it is 
an induced charge. If C were originally charged negatively the 
induced charge on AB would be positive. 

Observe that although one end of AB has a positive charge, 
and the other a negative, due to the presence of C, AB will be 
everywhere at the same potential, which will be higher than if 
the charge on C were not present. 




ELECTROPHORUS 



223 



Experiment No. 70, page 297. — This is a suitable method of charging 
an electroscope. The inducing body may be a rod of glass or wax held in 
the hand, for the charge on the end will not be discharged since the rod 
is a non-conductor. 

Experiment No. yi, page 298. — Electrification of water jet. 
Experiment No. 72, page 298. — Electrophorus. 

165. Electrophorus. — The charging and discharging of the 
cover of the electrophorus is explained in elementary books, and 
also in Experiment No. 72, but why the recharging of the cover 
from the disc can go on indefinitely, thus affording apparently 
an inexhaustible supply of energy without exhausting the charge 
on the disc of wax, is not always understood. When the free 
charge of the upper surface of the cover has been discharged to 
earth, a definite attraction exists between the disc and its cover. 
The removal of the cover does not alter the charge upon either, 
but work must be done to separate them (apart from the work 
of lifting against gravity) and when they are separated they 
possess energy of electrical separation equivalent to the work 
required thus to separate them. The discharge of the spark is 
the dissipation of this energy, but it is renewed in the next charge, 
not at the expense of the electricity on the disc, but by the 
mechanical work done in separating the cover from the disc. If 
the cover were not first put to earth, no work would have to be 
done against elec- 
trical forces to sep- 
arate the bodies 
and the cover 
would possess no 
electrical energy. 

Replacing the 
discharged cover 
upon the charged 
disc and repeating 
the transfer of 

electrification to Fig. 96. Toepler-Holtz Electrical Machine, 

another body with the electrophorus is an intermittent opera- 
tion, but by suitable mechanical contrivances the operation may 




224 POTENTIAL; MAGNETISM; ELECTRICITY 

be made continuous, and we then have an electrical machine. 
The most approved are the Toepler-Holtz, and the Wimshurst 
machines, for the description and explanation of which see 
larger treatises on Electricity. 

(Exhibit electrical machines, electrical gas lighter, etc.) 
166. Condensers. — Suppose a body be charged positively 
to a definite potential. This will require a definite quantity of 
electricity, and means that a definite amount of work is needed to 
bring a unit of positive electricity up to the body. If, however, 
a body charged negatively be put near the first body, it is evident 
that the work of bringing a positive unit to the first body will 
be less than before, or the potential of that body is lowered by 
the proximity of the opposite electrical charge. To raise the 
first body to the same potential as before will now require a larger 
charge upon it. In Fig. 95 if C is the body with positive charge 
and AB is brought near it, by putting B to earth the minus charge 
induced at A thus lowers the potential at C, and C must now have 
a larger charge to restore it to its former potential. Such an 
arrangement, by which a large quantity of electricity is necessary 
to produce a small rise of potential, is called a condenser. The 
actual quantity needed to raise the potential one unit is its 
capacity, and this depends upon the extent of surfaces opposite 
to each other, the distance between the surfaces and the nature 
of the dielectric between them. A common form is two sheets 
of tin foil with a glass plate between them. The thinner the 
plate of glass and the larger the sheet of metal the greater the 
capacity of the apparatus. 

Leyden Jar. — If such a plate condenser could be bent into the 
form of a deep bowl or jar it becomes the apparatus commonly 
known as a Leyden jar. A condenser is charged by means of an 
electrical machine by putting one plate to one pole of the machine 
and the other plate to the other pole or to the earth, — better 
put both the other plate and other pole to earth. With the Ley- 
den jar, merely holding the external coating in the hand is putting 
it to earth, and the other coating is brought to either pole of the 
machine by the knob which is in metallic connection with the 



ENERGY OF CHARGE 225 

inside coat of tin foil. Care must be taken by the operator not 
to touch the two coatings of a charged condenser at the same time. 
For discharging use a discharger, — a bent wire with a knob 
at each end and an insulating handle in the middle. 

Any arrangement of two conductors with a dielectric between 
them is a condenser in fact; the lecture room itself is such, the 
surface of any insulated body in it being one condenser surface, 
and that of the walls and objects in the room constituting the 
other surface. For fuller discussion of Arts. 165, 166, see Watson, 
Arts. 453-458 and especially Larden's Electricity, pp. 150-152. 

Illustrations. — Showing charging and discharging of condensers and 
Leyden jars; slow discharge; residual charge; human Ley den jar; jar with 
removable coatings; effects of disruptive discharge, etc. 

167. Energy of Charge. — If the quantity Q has been applied 
to a condenser, say a Leyden jar, to raise its potential from zero 
to V, the work required for this would be J QV, for if Q units were 
all raised to the potential V, the work would be QV, but if the 
first is raised zero, and the last to V, it is the same as if all were 
raised to the potential ^ V, and the work is Q times J V; and this 
would be the energy of its discharge. If such a jar, however, 
were put in connection externally with an equal, uncharged jar, 
and then its charge were shared with this second jar by connect- 
ing the knobs of the internal coatings, a single condenser would 
be formed of double the capacity of either of the jars. The same 
quantity of electricity would charge this condenser of double 
capacity to only half the former potential, or the potential of the 
large condenser would be \ V , and the energy would be \ (Q X J V), 
or \QV; that is, only one-half as great as before. With no loss 
of electricity one-half the energy has been lost. This loss of 
energy was the energy of the spark and noise when the two jars 
were connected. 

For "sparking distance" see Electrical World, Dec. 10, 1904. Below 10 cm. 
it varies with form and nature of electrode; for 10 cm. to 40 cm. the relation of 
voltage V to sparking distance d is given by the equation V = 4800 d + 24,000, 
where d is cm. and V is the maximum difference of potential in volts. At the dis- 
tance of 10 cm. this gives 72,000 volts, and for 40 cm. 216,000 volts before a spark 
will pass: from i\ to 2 mm per kilo volt. Vide infra Art. 221. 



226 



POTENTIAL; MAGNETISM; ELECTRICITY 



168. Lines of Force; Tubes of Force. — Arts. 168 to 174 
inclusive may be omitted on first reading. In electricity as in 
magnetism we may represent strength of field by employing one 
line of force to the square centimeter in a field of unit strength, 
and with tubes of force a unit tube would be one whose cross 
section is of such area as corresponds to unit force. If there were 
one unit line of force to the square centimeter, then a unit tube 
would have a cross section of one square centimeter; if the field 
of force had a strength of ten units, there would be ten unit lines 
of force to the square centimeter, and a unit tube of force would 
have a sectional area of jq sq. cm. 

But a different method has been adopted. If A and B (Fig. 97) 
are two electric conductors charged with equal quantities of elec- 
tricity, A positively and B negatively, all the lines of force (not 

meaning unit lines) from A in- 
closing an area on which is a 
charge of one unit of electricity is 
called a unit tube of force, and 
this tube, extending to and termi- 
nating in the surface B, there 
incloses an area upon which is one 
unit of negative electricity. The 
unit line of force, in this view, is 
simply the axis line of the unit 
tube. Evidently there are as 
many such tubes or lines from 
any portion of a surface as there 
are units of electricity on that portion of surface, or as many 
to the square centimeter as there are units of electricity to the 
square centimeter. This latter quantity, the ratio of the electric 
charge to the area over which it is distributed, is called the 
surface density of the electrification; hence the surface density 
may be represented by the number of unit lines or the number 
of tubes of force that proceed from or to the electrified body 
per unit area. (See further, Watson, pp. 624-634.) 

Given a small sphere uniformly charged with q units of elec- 




Fig. 97. 



TUBES OF INDUCTION 227 

tricity, if this sphere is remote from other charged bodies it will 
have q tubes of force radiating from it and rilling the space 
around it. A spherical surface surrounding this small sphere at 
a distance r will have 4 irr 2 units of area, comprising the ends of 
q tubes of force; therefore the number of tubes per unit of area 

will be — ^-r • If the small charged sphere is extremely small we 
471-r 

may regard its charge as all at the center of the large sphere, and 

the force due to it at a distance r is - 2 ; this, too, is the strength 

of field at the distance r, that is, at the surface of the large sphere. 
Thus, since the number of tubes per square centimeter of this 

surface is ^ , and the strength of field is -^ , the value of ~ may 
4 7rr r r l 

be written — ^— X 4 w. Also if the area of cross section of a tube 
471-r 

is 5 square centimeters, the number of tubes per square centi- 
meter is - ; writing F for the strength of field, or the force at 

distance r from the small charged sphere, the expression 

i 2 =- J -;X47r 
r l 4 7tt~ 

becomes F = - • 4 w, or Fs = 4 w = constant. 

s 

The cross section of the tube is supposed to be perpendicular to 
the line of force or on an equipotential surface. 

169. Tubes of Induction. — The product of the electrical force 
into the area of a surface perpendicular to the direction of the 
force is called the " electrical induction " through that surface; 
and we see that the induction through a normal cross section of 
a tube of force is constant and equals 4 w. If we call a unit tube 
of induction one in which the induction is unity, the unit tube of 
force equals 4 w unit tubes of induction. Thus on each square 
centimeter of the surface of a conductor which is charged to a 
surface density cr, there will be 4 wa unit tubes of induction. 
(Watson, Art. 458.) 



228 POTENTIAL; MAGNETISM; ELECTRICITY 

170. No Electrical Force Inside a Hollow Conductor. — It may 

be shown theoretically and experimentally that no force is ex- 
erted upon a charged body within a hollow charged conductor. 
As there is no field of force in the interior of such conductor, no 
work is done in moving a charge about within the interior space. 
(For demonstration, see Watson, Art. 452.) 

171. Action of a Uniformly Charged Sphere, Externally. — If 
we have a sphere of radius R, charged with Q units of positive 
electricity, and remote from other charged bodies, its lines of 
force are radial and its tubes of force are cones with their vertices 
at the center. Q tubes will cover the surface 4 tR 2 at a distance 
R from the center, and the area on the surface of the sphere inter- 

cepted by each tube is • If R is the radius of a bounding 

surface, each tube would include one. unit of electricity in this 
surface, and the force at a point in a normal cross section of such 

tube, as shown in Art. 168, is F = — > 

s 

This is the same as the force that would be exerted at that point 
if the whole charge Q were concentrated at the center of the first 
(or charged) sphere. 

Hence the force at an external point due to a charged sphere is 
the same as if the charge were all at the center of the sphere. 

172. Capacity of a Sphere. — If a quantity of electricity Q is 

at a point, the potential at a distance R due to Q is ~ • If a sphere 

K 

is charged with Q units the force exerted by this charge at the 

surface (and, as may be shown, the potential at the surface) is 

the same as if the charge Q were at the center ; then the potential 

V of any point on the surface is V = ~ • By the capacity is 

R 

meant the quantity necessary to raise the potential of the con- 
ductor from zero to unity. In this case V can be unity only if 



DISTRIBUTION OF ENERGY IN AN ELECTRIC FIELD 229 

Q = R. So the capacity of a sphere is numerically equal to the 
radius, and unit capacity is the capacity of an isolated sphere, 
one centimeter in radius (about the size of an ordinary marble) . 
Examples. — 

1. A charge of 162 units is placed on a sphere of 9 cm. radius, and an 
equal charge on a sphere of i-cm. radius. What is the potential of each 
spherical surface, and what is the energy of each charge? 

Ans. 18 and 162; 1458 ergs, and 13,122 ergs. 

2. In Ex. 1, what force would be exerted by the charges on the spheres 
against a unit quantity at a point 1 cm. distant from the surface of the 
sphere? Ans. 1.62 dynes; 40.5 dynes. 

173. Distribution of Energy in an Electric Field. — If A and 

B (Fig. 98) are two conductors constituting a condenser, and 
B is at zero potential while A has potential V due to charge Q, 
the total energy of the condenser is 

QV 

- — and the number of tubes 
2 

emerging from one plate and termi- 
nating on the other is Q, so that 

V 

the energy in each tube is — . It 

2 

may be shown that of this energy, Fi s- 98. 

the amount per unit length of the tube at any point n is 

equal to one-half the force F exerted at that point. The cross 

section of the tube here is ^ , and the volume per unit length 

r 

-p 

then is ~- c.c. But the energy per unit length is — , therefore 
F 2 

~ c.c. of volume contain — ergs; or the energy per cubic centi- 
F 2 

meter, where the force is F, is 

F 4* F 2 

2+t> or s; ergs - 

Again, suppose the tube to be divided by equipotential sur- 
faces, as in the figure, at every successive unit difference of poten- 

y 

tial. There will be V cells in the entire tube, and as there are — 

2 




230 



POTENTIAL; MAGNETISM; ELECTRICITY 



ergs in the entire tube, the energy in the tube for each cell, 
i.e., for a fall of one unit potential, is J erg. (See Watson, 
Art. 460.) 

To account for the actual distribution of the tubes of force in 
a field, and consequently for the forces to which bodies in the 
field are subjected, it requires that if F is the force at a point P, 

F 2 

then the tension in the air across unit area is — and at the same 

8 7T 

time a pressure equally great is exerted at right angles to the 
lines of force. (See Watson, Arts. 462, 463.) 

174. Electrometers. — The principles which we have thus far 
presented enable us to make many comparisons of potentials, 
fields of force, etc., but do not determine absolute values. We 
have not yet seen how to determine the quantity of electricity 
in a charge or the potential difference between two conductors. 

An instrument which would 
measure these in terms of a 
given unit of quantity or 
potential would be an elec- 
trometer; if it will measure 
them in terms of mass, 
length and time, or in me- 
chanical units derived from 
these, as force, it would be 
called an absolute electrom- 
eter. Various instruments have been devised for these pur- 
poses, of which one that has most commended itself is known 
as the attracted disc electrometer or guard ring electrometer. 
It employs directly the fundamental relation of electric attraction 
or repulsion, and the relation of the force to the distance and 
quantity of charge. Two circular plates AB and CD (Fig. 99) 
are placed parallel to each other, and from the upper one a cen- 
tral disc E is cut out so as to be separated from the annular ring 
around it by a narrow gap. The upper plate, both ring and disc, 
is connected to a charged body by a conductor, as a wire, and 
comes to the same potential with this body. The other plate AB 




Fig. 99'. Guard Ring Electrometer. 



ELECTROMETERS 23 1 

is connected to a body of opposite charge and comes to the same 
potential with it. 

If the distance d between the two plates is small the distribu- 
tion of the lines of force about the edges will not affect that in 
the central portions where the field will be uniform, and we may 
call the charge per unit area, i.e. the surface density, a. Call the 
area of the disc E = S. This disc will be attracted by the plate 
AB, and the force/ of this attraction may at once be deter- 
mined by having E suspended from an arm of a balance or from 
a spring. As there are a tubes of force for each square centimeter, 

the area of each tube is - sq. cm. Also the electrical force F at 

(7 

any point between the plates is 4 ira, and the force exerted by 

p 
each tube upon the plate E is — (Watson, Art. 463). The total 

2 

number of tubes on E being Str, the total attraction of the plate 
£is 

/ = . But F = 4 7T0-, 

2 

therefore / = 2 tSg 2 . 

Also in the uniform field of strength F or 4 tt<t, the work to carry 
a unit charge a distance d, i.e., from plate AB to plate E, is 
4 wad; but this means the difference of potential between the 

V 

plates, or 7 = 4 irad, hence a = — - , and this, substituted in 

4ird 

V 2 S 
the equation for /, gives / = - — — , 

8 ird 



whence V = y ^ > 

in which d and S are known in centimeters and square centi- 
meters, and /is weighed in dynes. Then V is electrostatic differ- 
ence of potential in ergs. 

This form of apparatus, variously modified and much elabo- 
rated, is a standard means of determining absolute difference of 
potential. From the dimensions of the plate E and its distance 



232 POTENTIAL; MAGNETISM; ELECTRICITY 

from AB, its capacity is calculable; therefore the quantity with 
which it is charged when the other plate is at zero potential (or 
to earth) is calculable. 

Electrokinetics. 

175. Current Electricity. — Thus far we have considered elec- 
tric fields of force and distribution of energy only under static 
electrification, or electrostatics. When, however, a transfer of 
electrification is going on along a conductor, work is being done 
and the field is changing unless a supply of electricity is kept up 
by some agent. Electricity passes by a conductor from a point 
of higher potential to one of lower potential, and if the difference 
of potential is to be maintained between the ends of the conductor 
some instrumentality must act to do it. The measure of its 
action in maintaining a difference of potential is called the elec- 
tromotive force, or E.M.F., and the passage of electricity along 
the conductor is a current of electricity. The science of elec- 
tricity under these conditions is Electrokinetics, or Current Elec- 
tricity. Whatever it is that passes from one point to another to 
constitute what is called a current, work is done, and the energy 
thus developed appears in the production of heat, or mechanical 
work, or chemical change. The transfer of electrification is 
found to be of the same nature as in the case of electrostatics, 
for, by connecting the two terminals of the current generator 
(battery or dynamo) to the two plates of a condensing electro- 
scope,* the plates are charged to the same potential as the poles 
of the generator, and when the latter are disconnected and the 
upper plate of the electroscope is removed, the instrument is 
found to be charged electrostatically and to give the same in- 
dications of attraction or repulsion when in the vicinity of a 
body charged with static electricity as if the condenser had 
been charged by a static machine or by contact with a statically 
charged body. 

* In a condensing electroscope the knob of the ordinary gold-leaf electroscope 
is replaced by a metal plate, 8 or 10 cm. in diameter, on which rests a similar plate 
with an insulating handle, like the cover of the electrophorus. 



DIFFERENCE OF POTENTIAL; ELECTROMOTIVE FORCE 233 

Experiment No. 73, page 299. — Electrification of a condensing electro- 
scope by means of battery cells. 

Thus the nature of the. electricity transferred by a current is 
not different from that of electricity at rest, nor does potential 
difference mean anything different in the two cases, though the 
field of force around a conductor is found to be greatly altered 
by the passage of a current. 

176. Electric Circuit. — An electric circuit, which is necessary 
for a continuous flow of electricity or a continuous current, con- 
sists of a generator in the form of a battery or a machine to main- 
tain a difference of potential between its terminals, called poles, 
and a conductor connecting the poles externally. The action of 
the generator may be chemical, or mechanical, or thermal, and 
for a current to pass there must be a completely connected series 
of conductors between the poles externally and through the gen- 
erator internally. When one pole is raised to a higher potential 
than the other, if there is no gap in the outer part of the circuit, 
electrification is transferred from the higher to the lower pole 
(called respectively + and — ) and that would be the end of the 
process if it were not for the action of the generator in again or 
continuously building up the potential of the + pole. In doing 
this the electricity is said to be carried or forced through the 
machine also. By way of illustration this is compared to the 
mechanical operation of a pump which continually lifts water 
from a well (negative pole) to a height of discharge (positive 
pole), from which it flows back by external circuit to the well. 
(Read Watson, Art. 472.) The circuit as a whole comprises the 
conductors that are external to the generator, and those by which 
the current is carried through the generator. For convenience 
these are sometimes called the external and the internal circuit 
respectively. 

177. Difference of Potential, and Electromotive Force. — 
From the experiment with the condensing electroscope, Art. 175, 
it was seen that the electricity transferred between the poles of 
a generator is of the same character as that produced by friction, 
and, therefore, by means of an absolute electrometer the difference 



234 POTENTIAL; MAGNETISM; ELECTRICITY 

of potential produced by the generator may be determined. The 
highest difference of potential the machine can produce is that 
between the terminals when the external circuit is open, and this 
is the measure of its electromotive force. It is, of course, a quan- 
tity of the same sort as potential difference, and therefore poten- 
tial difference and electromotive force are measured in the same 
units. Difference of potential is between any two points and 
is applied to the passage of a current through any specified part 
of a circuit; electromotive force is at the source of energy and is 
applied to the passage of a current through the entire circuit. 

Of course, to raise a quantity of electricity from a lower to a 
higher potential means to do work, and when electricity passes 
from a place of higher to one of lower potential it expends energy. 

178. Sources of Electromotive Force. — Electric difference 
of potential represents energy of electrical separation which is 
maintained by electromotive force. The chief sources of E.M.F. 
are: 

Chemical combination, in which energy of chemical separation 
is transformed into energy of electrical separation. 

Heat, in which thermal energy is transformed into energy of 
electrical separation. 

Mechanical work, in which mechanical energy is transformed 
into energy of electrical separation. 

The first of these is exhibited in voltaic batteries, the second 
in thermopiles, and the last in dynamos. 

179. Choice of Units. — Certain phenomena associated with 
the field surrounding a conductor that is carrying a current give 
a basis for comparing or measuring quantities of electricity, 
capacities, potentials, or other electrical magnitudes in a different 
way from that employed in electrostatics, and employing a 
different set of units. Of course, since the things measured in 
the two cases are of the same nature, the unit for any of the mag- 
nitudes in one case must have a definite and unvarying ratio to 
that for the same magnitude in the other case, just as the units 
of the British system of weights and measures have a definite 
ratio to those of the French system — the pound to the kilogram 



OERSTED'S EXPERIMENT 235 

or the yard to the meter — although if we are going to confine 
ourselves to the use of one system we do not need to know any- 
thing about its relations to the other. For absolute measure- 
ments, however, we still call the erg the unit of work or energy, 
and then choose such a unit for difference of potential, and such a 
unit for quantity transferred by the action of a generator, that 
to transfer that unit quantity through that unit rise of potential 
will require one erg of work; but the unit quantity here is much 
larger and the unit of potential much smaller than the corre- 
sponding electrostatic units. 

180. Oersted's Experiment : Field of Force about a Conductor 
Carrying a Current. — When a current is flowing in a conductor 
the region around the conductor is found to be thereby converted 
into a magnetic field of force. The transfer of energy along a 
conductor is at once attended by a field of force about the con- 
ductor. This field is manifested by the exertion of force upon a 
magnetic pole placed in it, a north pole being impelled in one 
direction, and a south pole in the opposite direction, but neither 
one either directly towards or from the conductor. A magnetic 
needle with opposite poles to be acted upon places itself in a 
plane at right angles to the conductor, the direction in which 
either pole alone would move being in a circle about the con- 
ductor. For a plane at right angles to the conductor, this field 
is readily shown by iron filings that arrange themselves in circular 
whorls. 

Experiment No. 74, page 299. — To illustrate magnetic field around a 
conductor. 

The discovery of this connection between electricity and mag- 
netism is due to Hans Christian Oersted (Danish physicist, 1820), 
and is shown by placing a magnetic needle above or below or 
alongside the conductor through which the current is passing. 

Experiment No. 75, page 300. — Illustrating the deflection of a magnetic 
needle by a current. 

With the usual convention that assumes the direction of the 
current to be from the positive to the negative pole of the battery 
through the external part of the circuit, the direction of the lines 



236 POTENTIAL; MAGNETISM; ELECTRICITY 

of force or the direction in which the positive pole of the needle 

would be urged is given by either of several rules; e.g., Ampere's 

rule : Imagine yourself swimming in the current, with the current, 

and facing the needle; the north pole will be deflected to your 

left hand. Also the letters spelling the word SNOW are initials 

of the words South, North, Over, West; i.e., if the current is from 

South to North Over the needle, it points West. 

The strength of field at any distance r from the conductor 

carrying the current, i.e., the force which would be exerted upon 

a unit magnetic pole, is proportional directly to the strength of 

the current ; this is made apparent by placing a second conductor 

carrying an equal current along with the first, and observing that 

the force on the pole is then doubled, and so on. The strength 

of field due to any small element of the conductor is inversely 

proportional to the square of the distance from the element to 

the magnetic pole. In Fig. 

1 00(a), if the current C is 

traversing the conductor 

AB, the force on a unit pole 

at m due to the element ds is 

kC ds sin , . . . ., 

; ds sin 6 is the 

r 

equivalent of the length of the 

element at right angles to r. 

If AB forms the circumference of a circle of radius r, then every 

element would make an angle 6 = 90 with r, and the force at the 

kC ds 
center due to each element would be — — . If the current were 

r 

flowing in a horizontal plane as indicated in the figure (b) , a posi- 
tive pole at m would be urged downward through the plane of the 
circuit. The total force on the pole for the entire circumference 

i i i kC ^\ , kC 2-KY k 2 ttC Tr , . ■. 

would be — V ds, or — , or . If we choose a circle 

of one centimeter radius the strength of field at the center is 
k 2 7rC, and since the effect at m is alike for all equal parts of the 
circumference, if we choose out one centimeter length of the arc, 




THE TANGENT GALVANOMETER 



237 



that is, -*- part of the circumference, the force at m due to this 

2 7T 

one centimeter of the arc is — part of k 2 irC, or F = kC. Now 

2 T 

by choosing for our unit current a current of such strength that, 
in such a case as this, F shall equal unity, then k = 1, and for the 
force at the center of a conductor in the form of a circle the force 
on unit pole, or the strength of the field, 

r 

181. Unit Current. — Definition : In the c.g.s. electromagnetic 
units, then, unit current is a current of such strength that, flow- 
ing in a circle of one centimeter radius, it exerts on a unit mag- 
netic pole at the center a force of one dyne for every centimeter 
of the circumference. There is no special name for this unit, 
except the electromagnetic 
unit of current strength, but 
a current one-tenth as strong 
as this is adopted as the 
"practical unit" current 
and is named an ampere. 

If, in Fig. 101, m were the 
positive pole of a magnet 
whose other pole was far 
enough from the plane of the circuit to make the effect of the 
current upon it negligible, then, with a unit current flowing 
round the circle of one centimeter radius, it would require a force 
of 6.2832 (or 2 x) dynes at P, on a balance of equal arms for 
every unit of pole strength at m to displace m upward. 

182. The Tangent Galvanometer. — At the center of the 
circle the lines of force in the magnetic field created by the current 
are all perpendicular to the plane of the circle, and if the latter 
is of large radius, say, 20 cm. or more, the field for a distance of 
several centimeters from the center is practically uniform and of 

2 7rC 

strength . If such a circuit were set up in a vertical position 




Fig. 101. 




238 POTENTIAL; MAGNETISM; ELECTRICITY 

as in Fig. 102, with its plane in the magnetic meridian and a small 
needle suspended at its center, this needle, under the influence 
of the earth's magnetism, would place itself 
in the plane of the circuit when no current 
is flowing. The passage of a current in the 
direction indicated would urge n to the 
west and s to the east, and the needle 
would be deflected until the decreasing 
moment of this deflecting force was coun- 
terbalanced by the increasing moment of 
the restoring force of the earth's magnetism 
Fig. 102. The Principle on ns. (Observe, the forces do not change, 
of the Tangent Gal- k ut their moments do, owing to the change 
in the angular position of the needle ns.) 
It can be easily shown that the tangent of the angle of deflection 
d is directly proportional to the strength of the current, and if the 
strength of the earth's field is H and the circular coil has n turns, 
the current C is 

C= — tana. 

2 irn 

Thus if H is known, such an instrument as this enables us to 
measure the strength of a current flowing through it, in absolute 
units, and this instrument placed anywhere in the circuit meas- 
ures the current flowing in the circuit. It is called a tangent 
galvanometer. (See Watson, Arts. 479, 480, 481.) Even if H 

rH 

were not known, if it is constant the factor would be the 

2Tfl 

same with the same instrument wherever it is placed and differ- 
ent currents could be compared by means of it, for the currents 
would be in just the same proportion as the tangents of the angles 
of deflection produced by them. 

If such a galvanometer is to be very sensitive it would have 
to show a considerable deflection with a very small current C. 
This would be accomplished by making n very large and r small, 
which is not always practicable; if r is very small the field of force 



THE MOVING COIL GALVANOMETER 



239 




in the coil will be uniform only very near the center, making the 
use of a needle of any considerable size out of the question. The 
sensitiveness is, however, greatly in- 
creased by making the needle nearly 
astatic. 

The purpose is better served by a 
more recent form of galvanometer, 
D'Arsonval's, in which a strong mag- 
netic field, practically uniform, is due 
to the poles of a permanent magnet. 
Between these poles is suspended by 
a fine torsion wire or ribbon a coil of 
many turns of wire through which the 
current to be ob- 
served, or a known 
fractional part of 
it, is passed (see 
Art. 193, Shunts). 
The plane of the 
coil is parallel to 

the plane of the magnetic poles (see Fig. 103). 
With the passage of any current, the ten- 
dency is for the poles of the magnet to swing 
round until the magnetic axis is perpendicular 
to the plane of the coil carrying the current. 
But according to the third law of motion, by 
whatever force the coil pushes the magnet, 
by just so much force the magnet reacts 
to push the coil. If the coil is fixed and 
the magnet pivoted, as in the tangent gal- 
vanometer above described, the magnet is 
deflected; if the magnet is fixed and the coil 
can swing around, as in the D'Arsonval and 
other moving coil instruments, it will do so. 
For small deflections the current is proportional to the deflection. 
Fig. 104 shows the actual construction, A and B being the 



Fig. 103. Principle of the Mov- 
ing Coil Galvanometer. 




Fig. 104. (a). 



240 



POTENTIAL; MAGNETISM; ELECTRICITY 



poles of the magnet, and M a mirror attached to the coil, in which 
is viewed the image of a fixed scale, showing the slightest move- 
ment of the coil. 




Fig. 104. The D' Arson val Galvanometer. 



183. Unit Quantity. — With a unit current, as above defined, 
flowing in a conductor, the quantity of electricity passing a given 
section of the conductor in one second is, in the c.g.s. system, the 
unit quantity of electricity. There is no name for this unit, but 
a quantity one-tenth as great is the " practical " unit of quantity 
and is known as a coulomb. 

184. Unit Difference of Potential, or Electromotive Force. — 
A c.g.s. unit difference of potential between two points is such a 
difference of potential that to transfer the unit quantity from 
one point to the other requires one erg of work. This is known 
simply as the c.g.s. electromagnetic unit, but the " practical " 
unit is io 8 (or 100,000,000) times as great as this and is called a volt. 

185. Unit of Capacity. — A conductor has c.g.s. unit capacity 
if a charge of one unit quantity raises its potential one unit; if a 
condenser have one plate at zero potential, then one c.g.s. unit 
of electricity upon the other plate will produce unit difference of 
potential between the plates. The " practical " unit of capacity 
is much smaller, being only io~ 9 times the c.g.s. unit, and is called 
a jar ad. 



UNIT RESISTANCE 24 1 

186. Resistance; Ohm's Law. — These units, namely, current 
strength, quantity, difference of potential, and capacity, serve 
to measure all the electrical phenomena we have as yet considered. 
The strength of the current that will flow with a given electro- 
motive force, or the electromotive force that is required to cause 
a given strength of current, is found to depend upon some quality 
inherent in the conductor. If two points were connected by a 
perfectly conducting medium, no difference of potential could be 
maintained between them. The facility with which a conductor 
will convey a current is known as its conductivity, and the 
measure of the conductivity of a conductor is its conductance. 
The maintenance of a given difference of potential at the ends 
of a conductor is attended by a flow of electricity through it, a 
large current, if a good conductor; a small current, if a poor con- 
ductor. Since a perfect conductor would transmit the electricity 
perfectly, this defect in conducting power has been called re- 
sistance. It is of course the inverse of conductance; the less 
readily a conductor transmits a current, the greater its resistance. 

Dr. G. S. Ohm, in investigating the relations of electromotive 
force E, current strength C, and resistance R, found that the 
resistance is directly proportional to the electromotive force (or 
the difference of potential) between two points, and inversely 

E 

proportional to the current, i.e., R — k -— • This is known as 

Cx 

Ohm's law and is perhaps the most important generalization in 
connection with electric currents. If we define our unit resist- 
ance to be such a resistance of a conductor that unit E.M.F. 
already defined will send through it a unit current as already 

defined, then in the above equation we have i=&-or& = i; 

-p 

and always then, in terms of such units, we shall have R = — > or 

187. Unit Resistance. — In c.g.s. system, unit resistance is the 
resistance of a conductor such that c.g.s. unit electromotive force 
will send through it c.g.s. unit current. 



242 POTENTIAL; MAGNETISM; ELECTRICITY 

Now Ohm's law applies to materials regardless of the system 

of units employed, and if our practical unit of electromotive force 

is io 8 times the c.g.s. unit, and the practical unit of current is 

io -1 times the c.g.s. unit, it follows that the practical unit of 

io 8 
resistance is — — or io 9 times the c.g.s. unit. This large unit is 
io l 

called an ohm, and R (ohms) = — -r ~ • 

C (amps.) 

188. Practical Units. — We have now pointed out the basis 
upon which a set of units has been evolved, rationally correlated 
to one another, and correctly expressing the physical actions they 
are to measure. In practice it has been found convenient to use 
units that are definite multiples or fractional parts of the funda- 
mental ones. From here on we shall generally use the practical 
units already named with the addition of one or two to those 
that have been mentioned. 

Since the work or energy of transferring electricity is measured 
by the product of the quantity, Q, transferred, into the difference 
of potential, E, through which it is transferred, we would have, 
always, work (or energy) = EQ. In the c.g.s. system, unit quan- 
tity raised unit difference of potential equals one erg ; in practical 
units one coulomb raised one volt equals io -1 X io 8 or io 7 ergs. 
This unit is called a. joule. With a practical unit of current, one 
ampere, flowing between two points at the practical unit differ- 
ence of potential, one volt, one coulomb is transferred every 
second, and one joule of work is done, or one joule of energy is 
expended, every second. Rate of doing work is power or activity, 
and an activity of one joule per second is the practical unit called 
a watt. 

Although the fundamental units are derived from the electro- 
magnetic effects of a current, the current will produce other 
effects to an extent whose relations to the current producing 
them may be determined, and these actions might be taken as 
the basis of measurement. 

These relations are exhibited in the following tables (see Wat- 
son's Physics, pp. 773, 774): 



PRACTICAL UNITS 



243 



Quantity. 


Name of practical 
unit. 


Equivalent in c. g. s. units. 


Current 


Ampere 

Coulomb .... 

I Volt 


io _1 electromag. units. 
10- 1 


Quantity 


Electromotive force or potential 


IO 8 


difference 


Ohm 

Farad 

Henry 

Toule 

Watt '. .. 




Resistance 


IO 9 


Capacity 

Induction * 


10- 9 

IO 9 


Energy or work 


io 7 ergs. 

io 7 ergs per second. 


Power or activity 





The unit of induction will be explained later; see Art. 206. 



Auxiliary units in the practical system. 



Name. 



Megohm 

Microfarad. . 

Microvolt 

Microampere. 
Kilowatt*. . . 
Millivolt. . . . 
Milliampere. 



Equivalent in the 
practical system. 



io 6 ohms. . . 
io -6 farads. 
io -6 volts. . 
io -6 ampere 
io 3 watts. . 
io -3 volts. . 



Equivalent in c. g. s. units. 



IO" 1 
IO - 
IO 2 
IO - ' 



electromag. units. 



io 10 ergs per second. 



electromag. units. 



* 1 kilowatt equals 1.341 horsepower. 

In the effort to determine as accurate standards for the elec- 
trical units of measurement as possible, all these varied effects 
have been examined. The chemical action of a current in de- 
positing metal from a solution of a metallic salt has been care- 
fully compared with the practical unit as above derived from 
the electromagnetic unit. Also the electromotive force of 
battery cells constructed according to definite formulas, for 
standards, has been compared with the practical unit of E.M.F. 
as derived from the electromagnetic, and in accordance with such 
comparisons the following definitions have been adopted through- 
out the world for the practical units. They are known as Inter- 
national Legal Standard Units, and are legalized in the United 
States by act of Congress. They are as follows: 

The ohm, the resistance offered to an unvarying electric current by a 
column of mercury at the temperature of melting ice, weighing 14.4521 
grams, of uniform cross-section, and having a length of 106.3 cm. 



244 POTENTIAL; MAGNETISM; ELECTRICITY 

The ampere, that current which, under certain specified conditions, 
should deposit silver from a solution of silver nitrate in water at the rate 
of toVoVW of a gram per second. 

The volt, the }?M of the electromotive force of a Clark cell set up 
according to certain specified conditions and kept at a temperature of 
1 5° C. For Weston Normal Cell, see Art. 216. 

The coulomb, the quantity of electricity conveyed by one ampere dur- 
ing one second. 

The farad, the capacity of a condenser charged to the potential of one 
volt by one coulomb of electricity. 

The joule, the quantity of energy expended per second in one ohm by a 
current of one ampere. 

The watt, the rate of work represented by one joule per second. 

The henry, the induction of a circuit in which a variation of one am- 
pere per second induces an electromotive force of one volt. 

The standard specifications were published in 1895 and may be found, 
with other details, in the United States Revised Statutes. 

We shall not discuss battery cells as sources of current until 
later, but merely point out that a definite E.M.F. is produced by 
any combination of different materials between which chemical 
action occurs, and the E.M.F. in any case depends only on the 
nature and temperature of the materials constituting the battery 
cell, and not in any degree upon the size or quantity, so that cells 
may be constructed for standards of E.M.F., as the Clark cell 
cited above. 

Examples. — 

1. If the resistance of a conductor is 250 ohms and the difference of 
potential at its ends is no volts, what current is flowing through it? 

Ans. 0.44 amperes. 

2. If a battery cell have an internal resistance of 0.07 ohms, and an 
E.M.F. of 2.4 volts, how strong a current would it give through an external 
conductor (a) of one ohm resistance; (b) of 0.1 ohm? If the cell were 
guaranteed to give 30 amp., what would you understand by that? 

Ans. (a) 2.243 amps.; (b) 14.12 amps. 

3. What e.m.f. is needed to send a current of 0.2 amp. through a cir- 
cuit whose resistance is 2000 ohms? Ans. 400 volts. 

4. The resistance of the human body in many cases is less than 2000 
ohms, and a current of 0.1 amp. may be fatal, what voltage between two 
terminals of a current generator is dangerous? Ans. 200 volts. 



VARIATION OF RESISTANCE WITH TEMPERATURE 245 

189. Specific Resistance. — According to Ohm's law, R = — > 

which means that with a conductor of any given material, no 
matter how the conductor may be varied in size or in shape, so 
long as it is made of the same material, the resistance will equal 
the quotient of the difference of potential between the ends of 
the conductor by the strength of current that flows through it. 
If, however, two conductors, alike in size and shape, but different 
in substance, are subject to equal E.M.F., the current will not 
be alike in the two, one being said to have higher conductivity 
or lower resistance than the other. Further, with any given 
material, at a given temperature, the actual resistance varies 
directly with the length /, and inversely with the area of cross- 
section s, so that, in general, R = k -, where k is a constant 

s 

that pertains to the particular substance of which the conductor is 

made. If the ratio of - is unity, k = R, so that if the conductor 
s 

were one centimeter long and one square centimeter in area of 
cross-section, called a centimeter-cube (not necessarily the same 
as one cubic centimeter), k = R, and this value of k for any given 
substance at a temperature of o° C. is called the specific resistance 
of the substance. (Conductivity and specific conductivity are 
the reciprocals of resistance and specific resistance, respectively.) 

Pure metals and other solid conductors differ greatly from one 
another in specific resistance, this being another " constant of 
nature " of great importance. Extensive tables have been pre- 
pared, in which copper has the lowest resistance. A few values 
are here shown : 

Copper, 1 . 6 X io~ 6 ohms per cm.-cube at o°. 

Platinum, 8.2 X "" " 

Lead, 19.0X " 

Carbon filament, 4000 X " " " " 

Experiment No. 76, page 300. — Illustrating conductivity of liquids. 

190. Variation of Resistance with Temperature. — The specific 
resistance of a substance usually increases with a rise of tem- 
perature (exceptions are carbon and conducting liquid solutions), 



246 POTENTIAL; MAGNETISM; ELECTRICITY 

at a rate varying somewhat with different substances, but nearly 
constant for any given substance. 

If the resistance were plotted as ordinates, taking temperatures 
as abscissas, the curve showing the rise of resistance with rise of 



-300" -200° -100° 0° 100° 200° 300° 400° 

Fig. 105. Curve of Resistance. 

temperature resembles that of Fig. 105. The slope is nearly 
uniform, but the curve is closely represented by an equation of 
the form R = ^^ + a t + bt 2 ), 

in which, for metals, a is very nearly 0.0037 and b is very much 
smaller. If b could be neglected, the equation would make 

R = o at / = , or — 273 C, that is, at the absolute zero 

0.0037' /J 

of temperature, a singular coincidence if not a significant one 
with regard to the inherent nature of resistance. 

The actual temperature at which the equation for pure metals 
gives zero resistance is about — 300 C. It must be admitted, 
however, that the coefficients a and b are determined from obser- 
vations at temperatures too high to justify the application of the 
equation to extremely low temperatures. 

While all pure metals increase in resistance with a rise in tem- 
perature, solutions which are conductors and carbon among 
solids vary in the opposite direction, the coefficient for carbon 
being about — 0.0004 per degree centigrade. The specific re- 
sistance of alloys is usually higher than the average resistance of 
their constituents, and the temperature coefficient is smaller. 
It has been possible to make an alloy with manganese, whose 
resistance is practically invariable under varying temperature. 
Such a substance is especially valuable for constructing standard 
resistances. 



DIVIDED CIRCUITS 



247 



Examples. — 

1. An iron wire, with a resistance of 2.5 ohms at o° C, just begins to emit 
a dark red glow when carrying a current of 9.25 amperes. If the difference of 
potential between its ends then is 90 volts and the temperature of the hot wire 
is 525 C.j what is the temperature coefficient? Ans. 0.0055. 

2. If the temperature coefficient of the carbon filament in an incandescent 
electric lamp is —0.00044, the resistance at zero degrees 460 ohms, and the 
current 0.45 amperes when the lamp is at full glow under no volts, what 
is the temperature of the filament? Ans. 1070 C. 

191. Resistance Coils. — Lengths of wire of different resist- 
ances are wound on spools and assembled in convenient order in 
boxes, so that they may 
be inserted in a circuit, 
and, by connecting them 
in any combination, may 
produce any value of 
resistance up to their sum 
total. These are called 
resistance boxes, and such 
a set of resistances is to 
the electrician what a set 
weights is to a chemist. Fig. 106 shows such an arrangement, 
the terminals of the coils being attached to thick metal bars, 
each of which can be connected to the next by a metal plug. 
Any conductor inserted as a part of a circuit to control or vary 
the strength of the current by its resistance is a " rheostat," 
whether it has standard values or not. 

192. Divided Circuits. — If two resistances r x and r 2 are joined 
tandem or in scries, connecting two points A and B of a circuit, 

their combined resistance 
is r\ + r 2 , but if they are 
_». joined in parallel, i.e., 
each one connecting A to 
B, as in Fig. 107, evi- 
dently there is more 
opportunity for a current to pass from A to B than by 
means of either conductor alone if the other were not there, 




Fig. 106. Resistance Box, Showing Interior. 




C r 2 
Fig. 107. Divided Circuit. 



248 POTENTIAL; MAGNETISM; ELECTRICITY 

and so the resistance of this so-called " divided circuit " be- 
tween A and B is less than either r\ or r 2 . In this case not 
the resistance, but the conductance between A and B is the sum 

of those due to them separately, or — h - , which is 2 ; then 

r\ r 2 r x r 2 

the resistance between A and B is the reciprocal of this, or 

— 1 —^~ . In the same way, if the resistance of any number of 
ri+r 2 

branches connecting two points in parallel is r h r 2 , • ■ . r n , sepa- 
rately, the resistance of them all in parallel is the reciprocal of 



^1 r 2 



7) 



193. Shunts. — It is possible, by the last article, so to pro- 
portion the two (or more) branches of a divided circuit that each 
branch shall carry a definite part of the entire current that is 
flowing around the circuit. For suppose, in Fig. 107, a current 
C is flowing from A to B by the two paths AGB and ACB of 
resistances r\ and r 2 respectively. The same difference of poten- 
tial V n A applies to the current passing through r 2 as to that 
through ri, therefore the current through r 2 will be to that through 

r x inversely as the resistances, or as — . If r 2 is to transmit n 

r 2 

times as much current as r iy its resistance must be only - as great. 

n 

Suppose AGB to be a galvanometer of known resistance and it 
is desired that only T ^ 7 part of the current shall pass through 
the galvanometer; then ^% must pass by way of the branch ACB 
and the resistance of ACB must be only ^ as great as that of the 
galvanometer. Such a by-pass as ACB is called a shunt, and 
with a galvanometer of known resistance r, it is usual to have 
several coils in a box, whose resistances are J, g 1 ^, g^ of the 
resistance of the galvanometer. When one of these coils is joined 
in parallel with the galvanometer, the current through the latter 
will be ^0, ilss or 1 oVo °f tne t°t a l current. (See Art. 182, Sen- 
sitive Galvanometer.) When shunts are constructed as here 
indicated, a special set is required for any particular galvanom- 



HOW TO MEASURE THE RESISTANCE OF A CONDUCTOR 249 

eter, but an improved form has been devised by Professor Ayrton, 
so that a single box may be used for any galvanometer, consti- 
tuting what is known asa" universal shunt." 

Examples. — 

1. If the potential difference between the wires from a dynamo machine 
is maintained at no volts, and a lamp whose resistance is 225 ohms connects 
the wires, what current will it carry? 

If two such lamps are inserted in series to connect the mains, what will 
be the current? 

If the two lamps connect the mains in parallel, how much current will 
each carry, and how much will both take? 

Ans. 0.489 amp.; 0.244 + amp. 
0.489 amp.; 0.978 amp. 

2. If ten electric lamps are used two hours each night, each carrying 
0.42 amperes, how much electricity must be supplied per night? 

Ans. 30,240 coulombs. 

3. A battery has its terminals connected by a conductor of 10 ohms re- 
sistance, and by another branch through a galvanometer (Fig. 107) whose 
resistance is 100 ohms. If the e.m.f. of the battery is 2 volts and its re- 
sistance is s ohms, how great is the total current, and how great that passing 
through the galvanometer? 

Ans. Total, 0.142 amp.; through galvanometer, 0.013 amp., nearly. 

194. How to Measure the Resistance of a Conductor; the 
Wheatstone Bridge. — If it is desired to know how much resist- 
ance a conductor offers, it may be made part of a circuit which 
includes a galvanometer. A current is passed through the cir- 
cuit and the deflection of the galvanometer is observed ; then the 
unknown resistance is replaced in the circuit by a box of known 
resistances, and these are adjusted until the galvanometer shows 
the same deflection as before. The resistance then in circuit in 
the box is the same in amount as was offered by the conductor 
whose resistance was sought. This is known as the method of 
substitution, and is seen to be exactly like the " substitution " 
method of finding the weight of a body. There are various other 
methods of measuring resistances, but the most common of all 
is the so-called Wheatstone bridge method. 

If, in Fig. 108, B is a source of current, as a battery cell, and 
between two points, A, C, of the circuit, two branches, ADC and 



250 



POTENTIAL; MAGNETISM; ELECTRICITY 



A EC, are inserted, let V be the difference of potential between 
A and C. The heavy lines indicate thick metal bars of negligible 

resistance. For every 
point along the branch 
ADC, there is a corre- 
^ sponding point on the 
branch A EC at the same 
potential. Suppose E to 
be at the same potential 
as D. The four portions 
of the divided circuit 
have resistances which we 
may designate r h r 2 , r 3 
and r x , as in the figure. 
The same current, say c h is flowing through r\ as through r 2 ; 
and the same strength of current, say c 2 , is flowing through 
r 3 as through r x . If we call the potential difference between 
A and D, V±, this is also the potential difference between A 
and E. Similarly, if V 2 is the fall of potential from D to C, 
it is also that from E to C. The value of the current in any 
branch is the potential difference between its ends divided by 
its resistance; therefore 

Vi = v_ 2} 

r\ r 2 




Fig. 108. Wheatstone Bridge Diagram. 



and 






v 2 

' r. 



Dividing these two equations, member by member, we get 

— = — . If r x is unknown we can compute its value from this 
n r 2 

equation, provided r\, r 2 , and r 3 are known, or if, of these three, 
either one and the ratio of the other two are known. 

To apply the method, two points, as E and D, are joined by a 
sensitive galvanometer; one branch, as EC, consists of the con- 
ductor whose resistance r x is to be determined. Sets of adjust- 
able resistances are placed in the other three branches. 



VARIATION OF RESISTANCE 25 1 

(1) If r 3 and Y\ are kept at a fixed value, y 2 is varied until no 
deflection of the galvanometer is produced. E and D are then 
at the same potential, otherwise a current would pass through 
the galvanometer. If r 2 is too small, a current passes from D to 
E; if too large, a current passes from E to D deflecting the gal- 
vanometer index in the opposite direction; but when no deflec- 

Vi Y 

tion is produced the equality of ratios holds, viz., -* = — , in 

r\ r 2 

which r x is the only unknown. 

(2) r\ and y 2 might have been kept at a constant value and r 3 
varied until a balance, or no deflection, was obtained and again 
the same equality of ratios would apply, or 

(3) r z might be fixed in amount and both r\ and y 2 varied, one 
increased as the other is decreased, until the galvanometer shows 
no deflection. The second is the plan used in the P.O. box 
bridge, and the third is that of the British Association slide-wire 
bridge. 

195. Variation of Resistance a Means of Measuring Tempera- 
ture. — If a substance is found to show a consistent change in 
resistance through a wide range of temperature, the variation in 
resistance of such a conductor may be used for thermometry. 
Platinum is such a substance, and as platinum remains solid at 
a very high temperature, a coil of it suitably mounted on a non- 
conducting material, as clay or porcelain, may be placed in a 
furnace or, if suitably encased, may be inserted in a bath of 
molten metal, and the temperature may thus be determined by 
observing the increased resistance of the branch circuit of which 
the coil is a part. 

Further, if a fine strip of metal is made to be one arm of a 
Wheatstone bridge, in which a balance has been obtained with a 
very sensitive galvanometer, then, so exquisitely susceptible is it 
that the slightest change of temperature in this strip will disturb 
the balance. An instrument arranged for this purpose by the 
late Professor S. P. Langley has been employed by him to detect 
and measure very low radiant heat; among other instances, that 
of moonbeams. This instrument is called a bolometer. 




252 POTENTIAL; MAGNETISM; ELECTRICITY 

196. Current Sheet. — For ordinary thin conductors, such as 
wires, the fact that the resistance is inversely as the area of cross- 
section would indicate that the current does not pass over the 
surface only, but utilizes the entire body of the material alike, 
the lines of flow being in the interior the same as at the surface. 
If a current is led into a thin, broad sheet of a conducting sub- 
stance at one point and out at another, the direction of flow at 
any point of this conductor can be determined and continuous 
lines of flow traced out. 

Let MNPQ (Fig. 109) represent such a conducting sheet, 
liquid or solid, and suppose the current passes from A to B. 
By attaching one end of a conductor (which leads externally 

through a sensitive galva- 
nometer) at pi and moving 
the other end so as to 
trace paths along the sheet, 
a series of positions p 2 , p3, 

Fig.ioo. Lines of Flow in a Current Sheet. ^ may be found f()r 

which no current passes through the external circuit. These 
points then are at the same potential as pi, and a line drawn 
through them is an equipotential line. Any number of such 
equipotential lines may be determined, and then any line traced 
continuously from A to B, crossing the equipotentials at right 
angles, will be a line of flow. This does not mean that the 
flow is only on the lines thus traced, but that at any point on 
such a line the direction of the line is the direction of flow at 
that point. 

If the conducting sheet be a piece of blotting or absorbent 
paper soaked with a solution of metallic salt, as, for example, 
sulphate of zinc, over which are scattered fine zinc filings, a 
current flowing from A to B will show lines of flow by the electro- 
deposition of metallic zinc connecting the zinc particles, much 
like the iron filings in a magnetic field. Fig. 140 (page 304) 
shows such lines of zinc deposit. (See Art. 213.) 

In mapping equipotential lines, as in Fig. 109 above, the cur- 
rent between A and B may be a rapidly alternating one, as from 



MEASURING INSTRUMENTS 253 

the secondary terminals of an induction coil. In such case the 
galvanometer should be replaced by a telephone receiver; a 
rattling noise will be produced in it except when the terminals 
are at the same potential; then the sound ceases. 

197. Measuring Instruments. — The relation of the practical 
units to the electromagnetic c.g.s. units having been adopted, 
and standard values for the practical units having been legalized, 
quantities are now usually measured and expressed in those units, 
i.e., current in amperes, E.M.F. or potential difference in volts, 
resistance in ohms, activity in watts (or kilowatts), etc. These 
terms should not be confounded with one another. To talk of 
a current as so many volts is as bad as to speak of a period of 
duration as so many feet. 

The following example of misuse of terms is not much worse than can 
be found in newspaper accounts nearly every day: A man touched the end 
of a live wire and received a current of 1,000 volts. The potential of his 
body being about 12,000 ohms, it offered a resistance of a little over 0.08 
amperes. The passage of this current through him represented an activity 
of 80 microfarads. Whether his death was due to the heat produced, which 
was 80 joules, or to the electrical work of 19.2 calories per second, does not 
matter, since they are equivalents; and it would not matter to him in any 
case. 

The same quantities would be used in a corrected statement as follows: 
A man touched the end of a live wire at a potential differing from his own 
by 1,000 volts. He thereby closed a circuit, and, the resistance of his body 
being about 12,000 ohms, he received a current of a little over 0.08 amperes. 
The passage of this current through him represented an activity of 80 watts. 
Whether his death was due to the heat produced, which was at the rate of 
19.2 calorics per second, or to the electrical work of 80 joules per second, 
does not matter since they are equivalents, and it would not matter to him 
in any case. 

Ammeter. — An instrument whose index shows the strength 
of current in amperes is an ampere-meter, or, as it is more com- 
monly called, an ammeter. To make such an instrument satis- 
factory it should have a large carrying capacity and a resistance 
so low that its insertion in a circuit makes the current from a 
given source of E.M.F. not appreciably different from what it 
would be if the instrument were not there. In any case, the 



254 POTENTIAL; MAGNETISM; ELECTRICITY 

ammeter is joined in the circuit in series so that the current that 
is flowing through the rest of the circuit passes through it also, 
as at A in Fig. no. Of the many forms of am- 
meter that have been devised the most approved 
is a modified form of the D'Arsonval galvanom- 
eter (see Fig. 103), the current or a definite 
fraction of it going through a thick coil of low 
resistance (perhaps only a few thousandths of an 
ohm) that is delicatety pivoted between the poles 
1 B of a strong permanent magnet in the case or box 

of the instrument. The scale is calibrated so as 
to read the correct number of amperes for any deflection of the 
coil. The deflection is shown by a light pointer attached to 
the coil (see Fig. in). 

Voltmeter. — An instrument that shows the difference of poten- 
tial between two points directly in volts is a voltmeter (not 
voltameter). To apply such an instrument in practice its ter- 
minals are made to touch the two points whose difference of po- 
tential is to be determined, and its needle then moves over the 
scale to correspond to the actual difference of potential between 
the two points thus connected. The usual form of this instru- 
ment is just the same as that of the ammeter except that the coil 
suspended in the magnetic field is of very high resistance, some- 
times many thousand ohms. To serve its purpose properly the 
voltmeter, when applied, ought not to disturb the current that 
is already flowing, if any, or cause any change in the E.M.F. by 
virtue of its application. But it is seen that its indications them- 
selves depend on the current actually passing through it. This 
instrument could not be used in series like the ammeter, as such 
use would at once so greatly increase the resistance of the circuit 
as greatly to alter the current. 

If, in Fig. 112, B is a battery cell sending a current through a 
circuit CDEF, and it is desired to know the difference of potential 
between E and F, the voltmeter V is connected to these points in 
parallel, as shown in the figure, and shows its readings while the 
current is passing. But the line through the voltmeter is a 



MEASURING INSTRUMENTS 



255 




(b) Shows Movable Coil with Pointer. 
Fig. in. Weston Portable Ammeter. 

shunt to the part R 2 of the main circuit, and unless the resist- 
ance of V is very large, this double conductor 
from E to F will be appreciably lower in resist- 
ance than R 2 alone, the actual current from B 
will be increased, and the potential difference 
between E and F at the same time may be 
less than before the voltmeter was joined in. 
If, however, the resistance of V is very great 
compared to R 2 this alteration is negligible. 




* 



A\'B 
Fig. H3- 



E Vb a 
R + r R 




E R + r 
Vb a R 


*+i 



256 POTENTIAL; MAGNETISM; ELECTRICITY 

By applying the voltmeter directly to the terminals of a voltaic cell it 

shows very approximately the E.M.F. of the cell; not exactly, for when it is 

thus joined a small current passes through the instru- 

wmwFmw — 1 ment and the D.P. between the poles is not exactly 
equal to the E.M.F. of the cell with the circuit open. 
To make this plain, suppose, in Fig. 113, the cell AB 
has an E.M.F. of E, and an internal resistance r, and 
the circuit is completed by an external resistance R. 

For the external circuit alone, the difference of potential between A and 

Vb a 
B, Vb a , is such that C = — - . For the entire circuit the electromotive 

XV 

force E is such that the current C = — — — . Since these two values of C 

R + r 

are identical, 

This may be written 



Here it is seen that if E is to equal Vb a , either r must be zero, which is 
impossible, or R must equal infinity, which is the case only when there is 
no conductor joining A and B. If, however, R, representing the voltmeter, 
is sufficiently large the ratio of E to Vb a can be brought as nearly equal to 
unity as we please. (Voltmeter should be shown along with this discussion.) 

Wattmeter. — If a current of A amperes is flowing between two 
points whose D.P. is V volts, then A coulombs are transferred 
every second and VX A is the number of volt-coulombs, or the 
number of joules per second of work done electrically on the 
part of the circuit in which the fall of potential is V. An activity 
of one joule per second is called a watt, or one volt-ampere. An 
instrument which will indicate at once not the volts measuring 
the D.P. between two points of a circuit, nor the amperes measur- 
ing the current passing, but the product of these two quantities, 
will show the activity of the current, and is called a wattmeter. 
For further account of wattmeters, as well as of other less com- 
mon meters, refer to technical electrical engineering works. 

Resistance Coils and some other means of measuring resist- 
ances have already been described. Instruments which read 
off resistance directly in ohms are called ohmmeters; they need 
not be described here. 



HEATING ACTION OF A CURRENT; JOULE'S LAW 257 

Standard condensers of tested capacity are mounted in boxes 
like resistance coils and are used to test capacities by special 
methods of comparison. 

198. Heating Action of a Current ; Joule's Law. — The differ- 
ence of potential between two points of a circuit is the measure 
of the amount of work done in carrying a unit quantity of elec- 
tricity from one point to the other. If a current C is flowing , then 
C units per second are transferred from one point to the other, 
and if V is the difference of potential, VC is the work done per 
second. If V and C are expressed in electromagnetic units, VC 
is ergs per second. When no other work is done in this part of 
the circuit except to overcome the resistance of the conductor, 
the energy expended there is manifested altogether as heat. If 

V 

R is the resistance between the two points, by Ohm's law C = — , 

or V = CR, and the work (or heat) VC = C 2 R per second. In 
/ seconds the total heat produced is, in mechanical units, H = C 2 Rt. 
This fact was discovered experimentally by Joule and the equa- 
tion is a statement of Joule's law. We see here that it was 
deducible from the principles of potential, but its experimental 
determination was one of the things that established the theory 
of potential, and particularly that brought out the fact that elec- 
tric potential and heat were measurable in like terms, and that 
both were ultimately reducible to mechanical work. 

In the equation VC = C 2 R, if C is electromagnetic unit current 
and R is electromagnetic unit resistance, the performance of 
work represented by VC or C 2 R is one erg per second. If the 
current C is one ampere, i.e., jq an electromagnetic unit; and 
if R is one ohm, i.e., io 9 electromagnetic units of resistance, the 
product C 2 R will be the work of carrying one ampere through one 
ohm resistance, io~ 2 X io 9 , or io 7 ergs per second; and so would 
be the product VC if V is one volt, which is io 8 electromagnetic 
units of potential, for io 8 X io -1 makes io 7 ergs per second as 
before, io 7 ergs is an amount of work called a joule, which may 
also be expressed in calories, or electrically as one volt-coulomb, 
and when work is done electrically at the rate of one joule 



258 POTENTIAL; MAGNETISM; ELECTRICITY 

per second it is one volt-ampere, or an " activity " of one 
watt. 

Under the Mechanical Equivalent of Heat, Art. 109, we found 
that one calorie is equal to 4.19 X 10" ergs, and therefore we 
should find that one calorie, when produced by an electric cur- 
rent, should equal 4.19 joules, or, 1 joule = = 0.2387 calo- 

4.19 

ries. By immersing a coiled conductor in water, measuring 
carefully the current C flowing through the conductor, and the 
potential difference V that is maintained between its ends, we 
have the rate at which electrical work is being done, which is VC 
joules per second. By measuring the mass m of the water 
heated, and the rise of temperature t° that is produced in T 
seconds, we have the number of calories mt° developed; this 
divided by T gives the calories produced in one second, and this 
again divided by VC (the number of joules per second) gives 
the calories equal to one joule. Taking from our definitions the 
mechanical value of one joule as io 7 ergs, we can thus arrive at 
the determination of the mechanical equivalent of heat from an 
electric current. This work, carried out by Dr. Joule (1852-4) 
in determining the mechanical equivalent of heat directly by 
the work of descending weights, and then indirectly by electrical 
work, before electricity itself was on a scientific basis or any syste- 
matic electrical measurements were known, was the beginning 
of the correlation of various branches of physics in one general 
scheme of energy and was the foundation of modern physics. 

199. Localizing Work in a Circuit; Electric Lights, — If a 
circuit has in it a source of constant E.M.F., and the agent de- 
veloping the E.M.F. has small resistance, the external part of 
the circuit may be so made up as to make the resistance of any 
given portion of it great in comparison with the rest. As the 
same strength of current is flowing everywhere through the cir- 
cuit, the difference of potential between any two points will be 
exactly in proportion to the resistance in that portion. If the 
conductor at one point has small mass with high resistance, as a 
thin fiber or wire, the work, VC or C 2 R, expended there per sec- 



LOCALIZING WORK IN A CIRCUIT; ELECTRIC LIGHTS 259 

ond, will be large and the heating will be great. The filament of 
the incandescent electric lamp in its earliest form was a fine wire 
of platinum, but this was too expensive for general use. It gave 
place to a narrow strip of carbonized paper or bamboo fiber, and 
this was enclosed in a glass bulb from which the air was exhausted, 
to prevent the combustion of the glowing filament by the oxygen 
of the air. This was the standard form for about thirty years. 
It was, however, not very economical, as it carried a current of 
nearly one half of an ampere, with a potential difference of no 
volts at its terminals for a lamp of sixteen candle power. This 
was an activity of about fifty watts or approximately three watts 
per candle. Efforts are continually made to improve the lamp, 
and to-day the carbon filament has been almost wholly su- 
perseded by the tungsten lamp, in which a modification of tung- 
sten is used that has had the fiber toughened by a special process, 
and which gives not only much more light in proportion to 
the electric energy expended (ij to 2 watts per candle power), 
but a light that is whiter and more agreeable than that of the car- 
bon. By introducing nitrogen into the lamp bulb, the pressure 
upon the filament seems to check its disintegration, thus permit- 
ting a higher temperature and increased brightness. 

The Nernst lamp is a calcium compound, which becomes 
sufficiently conducting when hot to give a strong white light. 

If a circuit carrying a current is broken, the resistance in the 
gap becomes great, and any considerable air gap would be prac- 
tically nonconducting. At the instant of separating, however, 
the connection is momentarily only so weakened as to make a 
high resistance without actually destroying the current. Great 
heat is at that moment developed, even to the melting and 
volatilizing of the metal at the ends of the broken conductor. 
Separating the ends slightly further gives a space filled with 
incandescent gas of high resistance between terminals that are 
glowing white hot. The heat here is intense and the light is 
brilliant. This is an arc light, so called because the incandescent 
vapor between the terminals has a curved or arched form. To 
maintain an arc requires a difference of potential of thirty volts 



260 POTENTIAL; MAGNETISM; ELECTRICITY 

or more. A voltage of 40 with a current of 10 amperes between 
carbon terminals would have an activity of 400 watts and would 
give a light of 600 to 1000 candle power, or about one-half or 
two-thirds of a watt per candle. 

Experiment No. 77, page 300. — Illustrating localization of energy by 
chain of alternate links of, say, copper and platinum. 

Experiment No. 78, page 300. — Heating a wire by electric current. 

Since an excessive current in a circuit may be destructive, if 
not actually dangerous, precautions to prevent this are taken in 
any scheme of wiring. The maximum current allowable in any 
part of a circuit is determined, and then that part of the circuit 
is connected to the other portion by a piece of easily fusible metal 
which will be so heated by the maximum current as to melt, thus 
breaking the circuit automatically. Such a piece of metal is 
called a fuse plug. It is prepared in sizes suitable to melt under 
currents of from one-half an ampere to fifty amperes. (Lecturer 
exhibit and illustrate.) 

The electric arc possesses a threefold interest in that it displays 
much of a purely electrical nature as to potentials and currents; 
it produces the highest known artificial heat, even to the degree 
of volatilizing diamond, and it is the most powerful light that 
can be produced by man, (Exhibit.) 

Examples. — One joule produces 0.24 calorie, and an activity of one 
watt produces one joule per second. 

1. An electric lamp has a current of 0.4 ampere with a potential differ- 
ence of 115 volts; what is the activity of the current? At what rate is heat 
supplied to the lamp? Ans. 46 watts; 11.04 ca l s - P er sec - 

2. A wire of resistance 25 ohms carries a current of 5 amperes; at what 
rate is it absorbing heat? Ans. 1 50 cals. per sec. 

200. Systems of Electric Lighting. — The electric incandes- 
cent lamp has a low illuminating power, having been adjusted to 
a convenient unit for distribution, of about 16 c.p. This is some- 
times reduced to 8 c.p., or raised to 32 c.p., but these can all be 
employed upon the same system if they give their rated illumi- 
nation at the same potential difference between their terminals. 
The form that has come into general use requires about no volts, 



ATTRACTION AND REPULSION OF CURRENTS 261 

and such a voltage is produced and maintained by dynamo- 
electric machines to be described later. Since, however, a differ- 
ence of potential of over 500 volts is dangerous to life, not more 
than five such lamps could be put in series without requiring a 
voltage so dangerous as to preclude its use in households or where 
the lamps are to be manipulated frequently. Accordingly the 
incandescent lamps are arranged in parallel (illustrate), between 
mains that are large enough to require small E.M.F. for driving 
a large current through them, and the current is supplied by a 
dynamo machine so constructed as to maintain practically a 
constant electromotive force under a varying load. 

The arc light, on the other hand, cannot be maintained at all 
without producing illumination many times as intense as that 
from the 16 c.p. incandescent lamp. It is not, therefore, suitable 
for lighting in small rooms, but is better adapted to large halls 
or outdoor lighting. Also it requires at best only about fifty 
volts, and therefore a considerable number of such lamps can be 
put on one circuit in series, all taking the same strength of 
current. The dynamo used commercially for this purpose will 
generate ten to fifteen amperes with an E.M.F. of 1500 volts, and 
will therefore supply thirty arc lamps. In the " inclosed arc," 
the supply of air is almost cut off, and a much longer service is 
obtained from the carbons, with a current as small as five am- 
peres and a potential of eighty volts. (Further details of electric 
lighting as well as of distribution, three- wire system, etc., are 
more in place as features of electrical engineering. A few lantern 
slides might be exhibited.) 

201. Attraction and Repulsion of Currents. — We have seen 
that a conductor carrying a current is encircled by magnetic lines 
of force, showing a' magnetic field of force in the vicinity of the 
conductor. If another conductor, also carrying a current, be 
placed alongside the first, the two will attract or repel each other 
according as the currents are in like or unlike directions. In 
general it is said that two currents flowing both towards or both 
away from a given point attract each other, but if one flow toward 
and the other away from the same point they repel each other. 



262 



POTENTIAL; MAGNETISM; ELECTRICITY 



The circuits endeavor so to place themselves as to bring the lines 
of force parallel to one another and in the same direction. 



Experiment No. 79, page 301 
Experiment No. 80, page 301. 



■ Roget's Spiral. 
Attraction and repulsion of currents. 



201 



Induced Currents; Lenz's Law. — If two circuits are near 
each other, any variation of the current in one is attended by a 
variation of the current in the other. If neither circuit has a 
current flowing, then the producing of a current in one induces 
a current in the other so long as the first current is growing, but if 
the inducing current presently reaches a value at which it holds 
steady, then the induced current ceases. If there is a current in 
the first circuit and it falls off or stops, this decrease or cessation 
induces a current in the second circuit during the time that the 
first is decreasing, which of course is momentary if the first is 
suddenly interrupted. If a current is flowing in both circuits, 
any variation in one is attended by a variation in the other while 

the change is in progress. This 
induction is ascribed to the 
change in the magnetic field 
about the circuit in which the 
current is induced, for if AB 
(Fig. 114) is part of a con- 
ductor carrying a current in 
the direction A B, lines of force 
encircle it as in the figure, some 
of which circles will be large 
enough in circumference to include the neighboring conductor 
A'B' . The action between the electric current and the magnetic 
whorls is a mutual one. The establishing of the current creates 
the magnetic field, and the creation of such a magnetic field will 
produce the current, but with this remarkable difference, that the 
magnetic field persists so long as the current continues but the 
current due to the magnetic excitation exists only while the field 
is changing. This change in the strength of the magnetic field is 
evidently the source of the E.M.F. that sends the induced current. 




INDUCED CURRENTS; LENZ'S LAW 263 

In the figure, an increase in the current in AB causes more lines 
to encircle A'B' and a current is induced in the latter. The 
current thus induced is always in a direction such that it tends to 
oppose the action that produced it; thus, in the case here men- 
tioned, starting a current in AB, or increasing it, sets up a current 
in A'B' in the opposite direction, for with currents in opposite 
directions the conductors would tend to separate or move so as to 
diminish the field about A'B' . On the other hand, if a current is 
flowing in AB, say, in the direction AB, and is stopped, with that 
stoppage the lines of force about both conductors will vanish, but 
a current is instantly established in A'B' in the direction A'B', 
since this is the direction of a current in this conductor which 
would make an attraction of it toward AB, and a movement of it 
toward AB would be of a sort to prevent a diminution of the 
lines of force encircling A'B'. Similar effects are produced upon 
moving the circuits toward or from each other. If AB carry a 
current and A'B' is brought up to it, a current is induced in the 
latter in the direction B'A', as such a current gives repulsion from 
the former, or opposes bringing the two toward each other; but 
if the second conductor is removed from the first it has a current 
induced in it in the same direction as that in the first, since then 
the two exercise an attraction which resists their separation. 
These relations between induced currents and the change of 
magnetic fields are generalized in Lenz's law as follows: The 
currents which are induced in consequence of movements or other 
changes in an electromagnetic system are invariably in such a 
direction that they tend to oppose these movements or changes. 

Both AB and A'B' above are supposed to be parts of complete 
circuits, for it is only in such case that a current can flow. In the 
case of a circuit around which a current is flowing, all the magnetic 
lines of force due to that current penetrate the plane of the circuit 
in the same direction. In the illustrations mentioned, an in- 
crease in the lines of force about one of the conductors is attended 
by an increase in the number penetrating the other circuit and 
vice versa. That circuit in which the change is made arbitrarily 
is called " the primary circuit," or simply " the primary," and 









— r- 


A^, 1 






B 

Fig. us- 





264 POTENTIAL; MAGNETISM; ELECTRICITY 

that in which the change is induced is called " the secondary cir- 
cuit " or " the secondary." If the latter is not closed, then a 
change in the current of the primary will set up an electromotive 

force in the secondary result- 
ing in a corresponding poten- 
tial difference between A ' and 
B> (Fig. us). 

The amount of this poten- 
tial difference is determined 
by the rate at which the mag- 
netic field in A'B' is altered, 
i.e., by the number of lines 
of force per second introduced 
into or withdrawn from the partial circuit A'B' . This rate is 
great and the induced E.M.F., therefore, high if the current in 
AB is made or broken very suddenly. While we perceive the 
induction effects in the form of currents, it is better to estimate 
them by the induced E.M.F., since this depends only on the 
rate of change in the magnetic field, while the current depends 
not only on the E.M.F. that is induced, but also upon the 
resistance of the secondary circuit. This sort of induction is 
called electromagnetic induction to distinguish it from that due 
to a static charge of electricity, or simply electric induction. 

Experiment No. 81, page 302. — Electromagnetic induction of currents. 

Note. — We use the term "line of force" in measuring the strength of field to 
mean unit line of force, and understand the numerical strength of field to be repre- 
sented by the number of such lines per square centimeter. More recently the 
phrase "tubes of force" is being used to make the nomenclature in electromagnetic 
induction conform to that of electric induction. When this term is used a unit 
tube is a tube whose surface is composed of linear elements every one of which is a 
line of force in meaning but not in intensity as above described, and the sectional 
area of a tube of force is such that the strength of field in the tube multiplied by 
the area of cross-section is unity. There are then as many tubes to the square 
centimeter as there are units in the strength of field. This makes "tube of force" 
correspond exactly to the "unit line of force" and the tubes of force just as numer- 
ous as the unit lines of force, and distributed in the same way. The advantage 
in its use is that it represents a filled-up field instead of one of threads with vacant 
spaces between them. See Arts. 168, 169 and 173, also Watson, p. 707. 



MAGNITUDE AND DIRECTION OF INDUCED E.M.F 265 

203. Magnitude and Direction of Induced E.M.F. — A change 

of one unit line of force per second through a circuit corresponds 

to one unit, electromagnetic, of E.M.F., or the total E.M.F. 

developed is the total change in the number of lines of force 

divided by the time in which the change is effected. In the 

dN 
notation of the calculus, at any instant it is — • 

at 

If a conductor AAA A (Fig. 116) inclose a space one centi- 
meter wide perpendicular to the lines of force in a field of unit 
strength, one line of force (or tube of force) will pass through 

A A 

1 



Fig. 116. Induced E.M.F. 

this space in every centimeter of its length. If a conductor ab 
in contact with A A extends across the space and is moved 
along from left to right at the rate of one centimeter per second, 
the inclosed circuit aAAb will be penetrated by lines of force in- 
creasing in number by one per second, and an electromagnetic 
unit of E.M.F. will be generated in this circuit and will send a 
current around it. If the lines of force are positive upward, the 
current will flow from a to b. Also if AAA A is very heavy so 
as to be virtually of no resistance, there will be virtually one unit 
D.P. between a and b, and if ab have unit resistance the circuit 
will have unit current. 

Note. — If ab have a resistance of one ohm, io 9 c.g.s. units, it would have to be 
moved across the unit field with a velocity of io 9 cm. per sec. to send a unit c.g.s. 
current. With current recognized by its various effects without reference to re- 
sistance or to Ohm's law, the resistance of a conductor might be represented by 
the velocity with which it must be moved across a given field to produce the current. 

When a conductor is moved in a magnetic field of force so as 
to cut the lines of force, an E.M.F. is developed and, if possible, 
a current is produced whose direction may be determined by this 
rule (Fleming): 



200 



POTENTIAL; MAGNETISM: ELECTRICITY 



Point the forefinger of the right hand along the line of force; 
(i.e. in the direction a north pole would be urged); point the 
thumb in the direction the conductor is to be moved (i.e., across 
the lines of force) ; point the middle finger at right angles to the 
plane of the thumb and forefinger; it will indicate the direction 
of the induced current. 

Fore thuMb middle 

Force Motion Induced 

204, Magnetic Field of Force in a Solenoid. — When a series 
of turns of wire are wound on a cylinder, the leading-in and lead- 
ing-back wires being led along or parallel to the axis of the cylin- 
der, a current through 
this apparatus is virtu- 
ally a series of parallel 
plane circuits perpen- 
dicular to the axis, car- 
rying equal currents all 
in the same direction. 
This gives rise to a field 
of force represented by 
a bundle of lines along 
the interior of the sole- 
noid, constituting with- 
in the solenoid a strong 



(b) 





^^T^YYVYY^ 




sTn I) I) () I) () 1) ft 




/^L__ j \ 


\ ~~ .^y 




vc— — — — — nns* 


s ^^^^^^ 


^^^— _^> 



N 



N 



(a) Field of Force in a Solenoid. 

(b) Field of Force in a Solid Cylindrical Magnet. 

Fig. 117. 



magnetic field which would induce magnetism in a magnetic 
substance placed there. The lines of force external to the sole- 
noid are like those external to a bar magnet, but within the 
solenoid they are in the opposite direction to those within the 
material of the magnet, as shown in Fig. 117 (a) and (b). See 
Watson, Arts. 515, 516. 

Experiment No. 82, page 302. — Lines of force in a solenoid. 

205. Strength of Field in a Solenoid ; Electromagnets. — We 
have learned that a current in a conductor forming one turn 
around a circle produces within the circle a magnetic field of force 
perpendicular to its plane; and in a solenoidal coil of many turns, 



STRENGTH OF FIELD IN A SOLENOID; ELECTROMAGNETS 267 

a field whose lines thread through the coil parallel to its axis; also 
that a change in the strength of the current changes the strength 
of the field; also that with a given current the strength varies 
with the number of turns of the conductor; but we have not yet 
determined the actual strength of field due to a given current or 
given number of turns. The demonstration for this in the case 
of a solenoid is rather advanced for this course, but when the 
turns are virtually all in one plane with virtually the same radius 
for all, we saw, Art. 180, that at the center the strength of field 

is in c.g.s. units for one turn and for n turns it is . If 

r r 

the current is in amperes, A , then since one ampere is only one- 
tenth of the unit C the number to express C is only one-tenth of 
that to express A , and C in the formula is replaced by jq A , so 

the strength of field is . Within a solenoid of n turns and 

5' 
current C (electromagnetic) it may be shown that the strength 
of field in c.g.s. units is 4 irnC. (Watson, Art. 516, or Carhart's 
College Physics, Art. 609; or Carhart's University Physics, Part 
II, Art. 322.) In any case it is seen to be directly propor- 
tional to the strength of the current and to the number of 
turns of the coil. The actual strength given by the formulae 
above is that produced when the space inclosed by the coil 
is air. Of course such a magnetic field would magnetize by 
induction a piece of iron placed within it, and how strong 
the magnetic induction would be depends upon the magnetic 
properties of the iron, — its permeability and susceptibility, but 
the very presence of iron in the space results in a much larger 
number of lines of force threaded through it than were in the 
space when it was filled with air instead of iron. Such an iron 
core greatly strengthens the magnetic field inclosed by the 
electric currents, and itself becomes a powerful magnet. It is 
called an electromagnet. A break of the current or removal of 
the lines of induction at once destroys the induced magnetism. 
Nearly all magnetic effects in practice nowadays are produced by 
electromagnets, which can be varied in strength, or made or un- 



268 



POTENTIAL; MAGNETISM; ELECTRICITY 



made, or even reversed in polarity, at will. (Observe the current 
is not sent through the iron core but around it in insulated wire.) 

Instead of fuse plugs to prevent overloading a circuit, as de- 
scribed in Art. 199, the winding of an electromagnet is sometimes 
made part of the circuit, the armature being attached to a switch 
by which the circuit may be opened or closed. When the current 
is at the maximum allowable strength, the magnet is powerful 
enough to pull the armature to it and thus open the circuit. Such 
an arrangement is known as a circuit breaker. 

Illustrations. — Electromagnets, straight or yoke form; electric bells, etc. 

206. Self-induction. — An electric current manifests some- 
thing like inertia, comparable to the flow of water in a pipe, in 
its tendency to persist, or to react against change. Not only 
does a change in the current in one conductor induce a current 
in a neighboring conductor of a nature to oppose the action that 

brings it about, but the 
c 

D 



same thing occurs in 
the circuit in which the 
change is first made 
while the change is going 
on. If in the circuit 
ACDB (Fig. 118 (a)), 
the action of the genera- 
tor AB is increasing so 
as to make the current rise, a counter E.M.F. is set up in the 
circuit, tending to oppose this change; on the other hand, if 
the current already flowing is rapidly diminished or is inter- 
rupted, an E.M.F. is set up tending to continue the flow in its 
original direction. This effect is most readily seen when the 
circuit is actually broken, making a sudden cessation of the 
current, i.e., an extremely rapid removal of the lines of force from 
the circuit. Such an act, even when the current is not very 
strong and the E.M.F. producing it is perhaps only that of a 
single battery cell, will show a spark across the gap when the 
circuit is broken. This indicates momentarily a high difference 
of potential at the broken termini. It is as if the current around 





118. 



A B 

(b) 
Self-induction. 



THE ELECTRIC DYNAMO 



269 



from A to B would not stop at once when the conductor was 
broken, say between C and D (b), but continued to drain off 
electricity from D and pile it up at C sufficiently to break across 
the gap while it is very narrow. If by any means the strength 
of magnetic field within the circuit is great, and is destroyed by a 
break in the circuit, the E.M.F. of self-induction is great. If 
ACDB, therefore, were a coil of many turns the self-induction 
would be greater than for a single circuit, and if the coil had an 
iron core it would be further heightened. 

Experiment No. 8j, page 303. — Self-induction. 

The practical unit of self-induction is called a henry, and is 
defined as " the induction of a circuit in which a variation of one 
ampere per second induces an electromotive force of one volt," 
i.e., changes the lines of force in number io 8 per second. 

207. The Electric Dynamo. — Electric currents on a large 
scale for commercial uses are obtained by electromagnetic induc- 
tion. Let abed (Fig. 119) 
be a single turn of wire in a 
magnetic field, directed as 
in the figure and mounted 
so as to be rotated in this 
field. Suppose the ends of 
the wire to be attached to 
the two halves of a slotted 
ring AB, called a commu- 
tator, and the coil and 
slotted ring set rotating in 
the direction shown (top 
to the right). When in 
the position shown in the 
figure no E.M.F. is pro- 
duced, for at that instant 
the number of lines through 

the coil abed is not changing, and even for a considerable angu- 
lar movement the change in the number penetrating the circuit 




Fig. 119. Principle of the Dynamo. 



270 POTENTIAL; MAGNETISM; ELECTRICITY 

is small. In one degree there may be a decrease of, say, ten lines, 
though the total number through the circuit may be large. When 
the coil has moved nearly a quarter of a revolution, say 89J , or to 
nearly a horizontal position, the total number of lines penetrating 
it will be small, perhaps not exceeding fifty in all, but in the next 
degree of angular motion, i.e. to 90J , the number will have de- 
creased to nothing and risen to fifty in the opposite direction, 
making a change of one hundred, and in that time an electromotive 
force due to a change of one hundred lines will be acting to send 
a current round the circuit. The magnitude of E.M.F. developed 
is determined by the rate at which the field is altered. If the 
above change of one hundred lines were effected in one-thou- 
sandth of a second, it would be at the rate of one hundred thou- 
sand per second, which would produce one-thousandth of a volt. 
It would be vastly greater if instead of a single turn of wire the 
coil had many turns, the rotation were much more rapid, and the 
strength of magnetic field between the poles many times greater. 
An increase of lines through in the opposite direction causes a 
current around abed in the same direction as when they were first 
decreasing, but this ceases when dc comes into the place of ah. 
After that the number decreases, slowly at first, but this sends a 
current in the opposite direction through abed, and it would also 
be reversed through the external circuit but at this instant the 
sliding brush B comes into contact with the other half of the 
divided ring, and so does A, and consequently in the external 
part of the circuit the direction of the current is unaltered. That 
is the function of the commutator and also the meaning of the 
name. If, instead of connecting with semicylinders, the ends of 
the coil were connected each with a slender bar that was in con- 
tact one with the brush A and the other with B at the time the 
coil was generating its highest E.M.F. , and then these bars 
passed out of contact with the brushes, and if another coil at an 
angle with the plane of abed connected with another pair of com- 
mutator bars, that would come into contact with the brushes 
while this coil passed through the position of highest E.M.F., 
this, in turn, to be succeeded by a considerable number of such 



THE ELECTRIC DYNAMO 



271 



coils in planes radiating from the common axis of rotation, each 
with its own pair of commutator bars coming successively into 
contact with the brushes in their fixed position, the current would 
be all the time produced from a 
maximum E.M.F. The effect is 
multiplied by making a coil of 
many turns instead of a single 
turn of wire abed. 

If, instead of having a slotted 
cylinder as a commutator, d is 
connected with a continuous metal 
ring or collar which is in sliding 
contact with B, and a and A are 
similarly connected with another 
ring insulated from the first, then 
the external circuit will undergo 
the same alternations of current 
as does the armature circuit or 
rotating coil. 

The magnetic field might be 
due to a permanent magnet, or, 
as is commonly the case, a shunt 
circuit connecting A and B might 
carry a part of the entire current 
around the limbs of a horseshoe 
of iron making a strong electro- 
magnet. This would be a shunt 
dynamo. If the entire current is 
carried round the branches of the 
magnet in series with the arma- 
ture it makes a series dynamo. Fig- 120. 

The former is employed when a (a) The Series-wound Dynamo. 
Constant E.M.F. is desired with ^ The Shunt-wound Dynamo. 

/ \ 1 i ( c ) The Compound-wound Dynamo. 

a varying load (current), the lat- 
ter with a constant current but varying E.M.F. A combina- 
tion of series and shunt constitutes a compound wound dynamo, 




272 



POTENTIAL; MAGNETISM; ELECTRICITY 



which affords a more perfect adjustment of E.M.F. to current. 
The three types are shown in diagram in Fig. 120 (a), (b), (c). 

Except for small or isolated plants, the compound winding is 
almost always employed for dynamos, the other two modes being 
employed in motors (Art. 208). 

When the coils are wound longitudinally about an iron core 
rotating with the shaft, they form a " drum armature." Some- 
times they encircle a ring of iron, as in Fig. 121, their ends being 
led to commutator bars, but the coils themselves being connected 

in series so that the current 
in the armature coils is con- 
tinuous from brush to brush. 
This constitutes a " ring arm- 
ature " or a Gramme ring. 
The field of magnetic force 
then follows chiefly the iron 
of the revolving ring, and 
the change of lines of force 
through the coils varies as in 
the preceding case. The po- 
larity of the iron ring is fixed 
in position though the ring 
itself revolves with the coils. 
As one coil departs from its 
maximum generating position 
its contact with the brushes ceases and the next coil takes its 
place. Fig. 121 (from W Miner's Experimentalphysik) shows this 
diagrammatically. 

208. The Electric Motor. — In either form of armature of a 
dynamo, when a current flows in a coil of the armature the iron 
core is magnetized, its poles keeping approximately a constant 
position relatively to the poles of the field magnets, a position 
due to that of the armature coil at its maximum generating posi- 
tion. By so adjusting the position of the brushes upon the com- 
mutator that when a given coil has its terminals in contact with 
the brushes the poles of the armature core are in a position to be 




Fig. 121. The Gramme Ring. 



THE INDUCTION COIL 273 

strongly drawn by the poles of the field magnets, then a current 
sent through the winding of the field magnets and the armature 
from an external source will produce a strong pull, or " torque " 
(turning moment), upon the armature. When the latter has 
turned a short distance its poles are no longer in the most effective 
position; the coil carrying the current breaks contact with the 
brushes, but the succeeding one makes contact and takes the 
place of the preceding one and the first condition of polarity and 
torque is restored; this continues in indefinite succession, and 
the machine is an electric motor. For instance in Fig. 121, if 
current is led into the apparatus at K\ and out at K, there is 
always a N. pole in the iron ring at the left and a S. pole at the 
right, and the ring will revolve clockwise. 

The dynamo and motor are interchangeable. The dynamo, 
driven by mechanical power, is called a generator, and acquires 
an E.M.F. which will send a current if the circuit through the 
armature is completed externally. If a current is led into the 
dynamo from an external source it will drive the armature and 
furnish mechanical power as a motor. - The late Professor Clerk 
Maxwell is credited with saying that the greatest discovery of 
the third quarter of the nineteenth century was that the Gramme 
machine was reversible. 

Experiment No. 84, page 303. — Cycle of Energy-Changes. 

209. The Induction Coil. — A strong current may be produced 
by a low electromotive force in a circuit of low resistance, and 
if this is a coil as PP (Fig. 122) 
with an iron core, it will be pene- 
trated by a large number of lines 
of force. If the same coil is en- 
veloped by another coil, as SS, 
having a large number of turns, 
insulated from the first coil, the 
break of the current in the first 
or so-called " primary " circuit 
will induce a great E.M.F. in the second or " secondary " coil. 




b a 

Fig. 122. The Induction Coil. 



274 POTENTIAL; MAGNETISM; ELECTRICITY 

The sudden closing of the primary induces an E.M.F. in the 
opposite direction. The primary may be so arranged with a 
circuit breaker that the closing of the circuit and thus estab- 
lishing of a current actuates an electromagnet M which attracts 
an armature in the form of a spring so as to open the circuit at 
ab; then, the attraction of the magnet ceasing, the spring again 
closes the circuit, the electromagnet again acts, and so the 
make and break are continued automatically, precisely as in an 
electric bell, and the secondary has a high E.M.F. produced in 
it alternately in opposite directions. Such an apparatus is an 
induction coil. Instead of the magnetic automatic interruption 
the make and break is sometimes accomplished by an inde- 
pendent mechanical action. A form of interrupter, Wehnelt's, 
is sometimes employed in which the interruptions are produced 
by the formation of gas bubbles due to the passage of the pri- 
mary current through an electrolytic cell. 

If the terminals 55 of the secondary are separated, the differ- 
ence of potential between them may be great enough to cause a 
spark of considerable length to pass between them. Coils are 
in use capable of producing a spark a meter in length. 

As we have seen, the self-induction in the primary, as well as 
the induction in the secondary, tends to delay the rising of the 
current to its full strength when the circuit is being closed and 
to hinder the stoppage of the current when the circuit is being 
opened, and, especially in the break, a- spark carries on the current 
so as to make the interruption tardy. This is overcome by 
joining a condenser across the gap of the primary as at C in the 
figure. When the gap at ab is closed the current flows through 
the primary PP in the direction of the arrow. The magnet M 
at once pulls the armature b and opens a gap between a and b. 
The flow of self-induction which would expend itself in a spark 
bridging over the gap ab now goes to charge the condenser C, and 
the interruption of the primary is made more sudden and com- 
plete, as is seen by the diminution or almost complete extinction 
of the spark between a and b. On the return of b to close the 
circuit, the discharge of the condenser acts with the battery in 



TRANSFORMERS 275 

supplying energy to the primary and again helps the action of 
the coil, besides preventing the loss of energy that would have 
otherwise been wasted in the spark. The presence of the iron 
core II greatly increases the number of lines of force introduced 
into the circuit or taken out of it and, of course, vastly heightens 
the E.M.F. induced in the secondary SS. Whatever the value 
of this E.M.F. for a single turn of the secondary, it becomes n 
times as great for n turns, so that by making this number enor- 
mously large a high E.M.F. may be developed from a low E.M.F. 
in the primary circuit. But this effect is interfered with if the 
self-induction in the secondary is great; the secondary, there- 
fore, must have fine wire and its resistance becomes enormously 
greater than the resistance of the primary, so that, although the 
E.M.F. is large, the actual current in the discharge of the second- 
ary is small. This condition would be recognized in any case, 
since the energy of the induced current could not be greater than 
that of the current inducing it. The product of the E.M.F. by 
the quantity of electricity transferred measures this energy. In 
the primary there is a large current with a small E.M.F.; in the 
secondary, a large E.M.F. and a proportionally small current. 
Or, again, the magnetic field due to the primary is proportional to 
the ampere-turns of the primary current; the induced current is 
due to the formation or destruction of this same field, and if the 
dimensions of the two coils were alike this field would bear the 
same proportion to the ampere-turns of the secondary. The 
turns being large in number the current is small. 

The nature of the discharge from the induction coil, its charging 
of Leyden jars or other condensers, and other features of static 
electricity are like those produced by static electric machines. 

Illustration. — Exhibition and operation of induction coil. 

210. Transformers. — With two different sets of windings 
around an iron core, either one may be used as a primary and 
the other as a secondary. If one has, say, ten times as many 
turns as the other and the same change of magnetic field is 
effected in both, then a break of the current in the shorter circuit 



276 POTENTIAL; MAGNETISM; ELECTRICITY 

will induce an E.M.F. ten times as great in the other, and vice 
versa. A contrivance so arranged is called a transformer, and is 
a " step up " or a " step down " transformer according as the 
induced E.M.F. is higher or lower than that of the primary. 
For commercial transformers an alternating current is best 
adapted since that accomplishes the greatest change of field at 
a rapid rate. Electricity generated at a high potential is trans- 
mitted over a small conductor since the current is small even for 
a large transference of energy. Then by suitable transformers 
it is reduced to a voltage proper or safe for introduction into 
houses or shops. For heating and lighting the alternate current 
may be used as well as the direct; for power purposes, however, 
the motor that will work with an alternating current is not as 
satisfactory as the direct current motor, and therefore when 
electric power is sent out in alternating form it is used to drive 
one large alternate current motor which in turn drives the arma- 
ture of a direct current dynamo, either on the same shaft as its 
own, or by gearing to it. 

211. The Telephone and Telegraph. — Without going into 
particulars of central-station connections the principles of the 
telephone are shown in Fig. 123. A disk D is set vibrating 




Fig. 123. Local Battery Telephone Circuit. 

by the voice spoken into the transmitter A. This disk makes 
contact with one or more granules of carbon in the back of the 
instrument as at C. Varying pressure between D and C causes 
varying resistance in the circuit of the battery B through C, D, 
and the primary of a small induction coil /. The secondary of 
this induction coil forms a circuit to the distant receiver R. In 
this receiver a permanent magnet M has one pole encircled by a 
coil of fine wire which is part of the circuit with the secondary 



THERMOELECTRICITY 277 

of the coil at the transmitting station. Variations of the current 
in the primary circuit of / cause induced currents in the line to 
the receiving station. The magnet 'M attracts an iron disk V 
and the varying current through the line L causes correspond- 
ing variation in the attraction of M upon V, so that the latter 
vibrates in exact response to the vibrations of D. A duplicate 
arrangement in the sending and receiving stations makes the 
apparatus to work both ways. The circuit from B is open until 
the removal of the receiver from the hook closes the circuit. In 
most cases, now. the local battery B is replaced by a larger bat- 
tery at the central station. The telephone is essentially an 
apparatus of induced currents. 

The telegraph, on the other hand, is operated by electro- 
magnets, the signals being due to the making or unmaking of 
magnets by closing or opening an electric circuit by means of a 
key. Nearly all electric apparatus for mechanical purposes is 
operated in a similar manner by electromagnets. 

212. Thermoelectricity. — If a circuit be composed of differ- 
ent metals, say, two for simplicity, joined in series, and one 
junction is heated while the other junction is not changed in tem- 
perature, a current flows around the circuit. The electromotive 
force thus set up is called thermoelectromotive force, and two 
metals so arranged are called a thermocouple. Suppose the 
couple to consist of copper and iron. If one junction is kept at 
the ordinary temperature while the other is gradually heated, the 
current will pass from copper to iron through the hot junction 
and increase as the temperature is raised until it reaches a maxi- 
mum. With further rise of temperature the E.M.F. falls off and 
the current decreases. The temperature at which this maximum 
E.M.F. is reached is called the neutral temperature for those two 
metals. The decreasing current beyond this ceases when a tem- 
perature is reached that is as high above the neutral temperature 
as the unheated junction is below it. At a still higher tempera- 
ture the direction of the current is reversed. The rate at which 
the E.M.F. rises per degree of increase in temperature is called 
the thermoelectric power of the metals. It is, of course, different 



278 POTENTIAL; MAGNETISM; ELECTRICITY 

at different temperatures, being zero at the neutral temperature. 
It is different also for each different pair of metals. 

Antimony, iron, copper, silver, tin, lead, nickel, bismuth, form 
a series such that if a junction of any two be heated a current will 
flow from the earlier in the list to the later through the external 
circuit, provided the mean temperature of the two junctions is 
below their neutral temperature. The actual E.M.F. set up is 
low. The thermoelectric power and the E.M.F. for the various 
metals may be obtained from suitable tables and diagrams. An- 
timony and bismuth give the highest E.M.F. in the list. Taking 
lead as a basis to compare with other metals, the thermoelectric 
power of selenium is about thirty times that of antimony. In a 
copper-iron couple, as described above, if one junction is at 20 C. 
and the other at ioo° C, the E.M.F. is 524 microvolts, (0.000524 
volts). That is, a thousand such couples in series would have 
about one-half the E.M.F. of a gravity cell. (See Watson, 
Arts. 501-503.) 

Experiment No. 85, page 303. — Thermoelectric current. 

213. Chemical Effect of a Current; Electrolysis. — When a 
current passes through a liquid conductor other than metals, the 
liquid is decomposed. This effect of the current is called electrol- 
ysis, and the liquids electrolytes. They are usually dilute acids 
or aqueous solutions of metallic salts. The solid conductors by 
which the current is supposed to enter and to leave the liquid are 
termed electrodes; that by which the current enters is connected 
with the positive pole of the source of current and is called the 
anode, the other, by which the current leaves, is the cathode. 

Suppose the current to pass through the series of four vessels 
(Fig. 124), in which C contains dilute sulphuric acid with the 
electrodes inserted in two inverted tubes that are filled with the 
same liquid, D and E contain a solution of copper sulphate, and 
F a solution of silver nitrate. The electrodes in D are plates of 
copper, and those in C, E and F are sheets of platinum. When 
the current has been flowing for some minutes, equally strong 
everywhere, the tube over the anode in C will be found to contain 



CHEMICAL EFFECT OF A CURRENT; ELECTROLYSIS 279 

oxygen gas which has risen to the top of the tube, and that over 
the cathode will contain hydrogen gas in quantity twice as much 
as the oxygen, in D the copper anode will have been partially 
eaten away while the cathode will have metallic copper deposited 
upon it, the solution remaining little altered in concentration; in 
E the anode will have given off oxygen, copper will be deposited 
on the cathode, and the concentration of the solution will be 
diminished; in F oxygen will have been given off at the anode 
and silver deposited on the cathode, while the solution will be 




Fig. 124. Electrolysis. 

weakened. Electrolysis will have occurred in each vessel. 
Where the electrolyte is acidulated water, the result of dissocia- 
tion is simply hydrogen liberated at the cathode and oxygen at 
the anode ; in the case of many electrolytes, however, secondary 
chemical reactions occur in the electrolytic cell, but the final 
result is the liberating of one substance at one electrode and a 
different substance at the other. These final products in their 
elementary form are called ions, those which appear at the anode 
being anions, and those at the cathode cations. In the elec- 
trolysis of a metallic salt the cation is the metal that is in the 
compound. Its deposition on the negative electrode is electro- 
plating. In the experiment just described the cathode in D and 
E is plated with copper, and that in F with silver. 

Experiment No. 86, page 304. — Electrolysis. 
Experiment No. 87, page 304. — Current Sheet (see Art. iq6). 

The laws of electrolysis, as determined by Faraday, are as 
follows : 



280 POTENTIAL; MAGNETISM; ELECTRICITY 

(i) " The mass of an electrolyte set free by a current of elec- 
tricity is directly proportional to the quantity of electricity 
which has passed through the electrolyte." If m grm. of a sub- 
stance are deposited by the passage of q units of electricity, then 

• . m 

m is proportional to q, or the ratio of — is constant for that sub- 

stance. The mass deposited is the same by a weak current kept 
up a long time as by a strong current in a short time if the quan- 
tity of electricity transferred is the same. 

(2) "If the same quantity of electricity passes through differ- 
ent electrolytes, the masses of the different ions deposited will 
be proportional to the chemical equivalents of the ions." If the 
same current passes through acidulated water and solution of 
copper sulphate, for every gram of hydrogen liberated there will 
be 8 grm. of oxygen and 31.6 grm. of copper. 

The relation is simplified by referring at once to the electro- 
chemical equivalent of a substance, by which is to be understood 
the mass of the substance deposited by the passage of one unit 
of electricity. If we call the electrochemical equivalent g, and 
m grm. are deposited by q units of electricity, then the mass 

deposited per unit of electricity is — , or g = — . Now if the cur- 
rent strength is c and the time it has been in action is /, then 

q = ct, and g = — . Thus by observing the mass deposited in 
ct 

any length of time by a known current, the electrochemical equiv- 
alent of any substance may be determined. An instrument 
for such purpose is called a voltameter. By making such de- 
terminations with various substances it is found that their 
electrochemical equivalents are proportional to their chemical 
equivalents. 

If the current is measured in amperes, the unit quantity of elec- 
tricity is the quantity conveyed by a current of one ampere in one 
second, or a coulomb, and this quantity liberates 0.000010366 
grm. of hydrogen, which is therefore the electrochemical equiva- 
lent of hydrogen. Calling the chemical equivalent of hydrogen 



MIGRATION OF THE IONS 28 1 

unity, that of silver is 107.88, and accordingly the electrochemical 
equivalent of silver is 0.000010366 X 107.88, or 0.0011183. This 
rate of deposition of silver, it will be remembered, was made the 
basis of the international unit of current strength. (See Art. 188.) 
As many grams of a substance as the number expressing its 
chemical equivalent are called a gram equivalent of that sub- 
stance. A gram equivalent of silver is 107.88 grm., and to de- 
posit one gram equivalent of silver would require — , or 

0.0011183 

96,470 coulombs, and this is the quantity of electricity that will 
cause the separation of one gram equivalent of any kind of ion. 

Examples. — 

1. How many grams of hydrogen will be liberated in one minute by a 
current of 5 amperes through acidulated water? Ans. 0.003108 g. 

2. How much silver will be deposited from a silver solution in two hours 
by the passage of a current of 2 amperes? Ans. 16. 1 g. 

3. If a current of 3 amperes through a solution of copper sulphate de- 
posits 3.52 grams of copper in one hour, what is the electrochemical equiva- 
lent of copper? Ans. 0.000326. 

214. Migration of the Ions. — It is supposed that electricity 
passes through an electrolyte by a sort of convection, being car- 
ried by the ions, each cation carrying a definite positive charge 
in the direction of the current, and each anion a definite negative 
charge in the opposite direction. The theory requires the sup- 
position that there are always a number of free ions in the elec- 
trolyte, but it is possible to derive a pretty definite value for the 
velocity with which the ions travel. For example, in HC1 at 
18 C, with a potential gradient of one volt per centimeter, the 
migration velocity u of the cation H is 311 X io -5 cm. per 
sec; and for the anion CI it is v = 78 X io~ 5 cm./sec, a slow 
travel. A fluid in this condition is said to be ionized. Hydro- 
gen behaves as a metal. The whole theory of ionization includ- 
ing solution pressure and osmotic pressure is much too elaborate 
for presentation here. It plays an important part, however, 
in the theory of the voltaic cell. It is extensively treated in 
Watson's Physics, Book V, Part VIII. 



282 POTENTIAL; MAGNETISM; ELECTRICITY 

215. Polarization. — One result of the carrying of charges by 
ions is to electrify the cathode in the liquid positively and the 
anode negatively, and to that extent to introduce a tendency to 
send a current in the reverse direction (sometimes called counter- 
electromotive force). In the simple acid- water voltameter, the 
cathode quickly becomes covered with bubbles of hydrogen and 
the anode with oxygen, the former being electropositive and the 
latter electronegative, and the difference of potential between 
the plates on that account may rise to more than two volts. 
Unless the external E.M.F. exceeds this, the current will weaken 
and finally cease. This effect is termed polarization. If such 
a cell be disconnected externally from its source of E.M.F., it is 
then itself capable of being discharged, something like a con- 
denser, and if its terminals be connected through a galvanometer 
a current is shown for a brief time by the latter, in the opposite 
direction to that by which the cell was charged. 

216. The Voltaic Cell. — Two unlike substances, when brought 
into contact, come to a different potential, called contact poten- 
tial difference. If two solids dip into a liquid conductor which 
acts chemically upon either of them, the final difference of poten- 
tial between the terminals of the metals, called " poles," will 
usually be higher than that when there is no chemical action. 

The typical arrangement for this is a plate of copper and one 
of zinc, not touching each other, in dilute sulphuric acid. If the 
zinc is pure (or if it is amalgamated with mercury) , it is attacked 
by the acid only momentarily until the copper pole, outside the 
acid, rises to a potential 1.08 volts higher than the zinc pole. 
Internally an equilibrium is established between the solution 
pressure of the metals in the acid and the electric forces due to 
the charged ions, and chemical action then ceases. When, how- 
ever, the poles are joined by an external conductor, electricity 
carried through it from copper to zinc destroys the equilibrium 
in the cell, and chemical action is resumed, the energy that is 
supplied being directly that of the chemical combinations taking 
place within the cell. Such an apparatus is a voltaic cell or ele- 
ment. In the course of its action the current passing from zinc 



THE STORAGE OR SECONDARY BATTERY 283 

to copper within the liquid polarizes the cell just as in electroly- 
sis, unless some means, chemical or mechanical, are devised to 
take up or get rid of the hydrogen that appears at the copper 
plate, or to neutralize the polarizing action. Some forms of bat- 
tery cells are made of materials which so act as to depolarize at 
the same time that they polarize. Such cells are called constant, 
and are of especial service where the action of the battery is to 
continue a long time without interruption. The best type is the 
Daniell or gravity cell. Others depolarize slowly, and regain 
their normal condition if allowed to rest after they have been 
used for a brief time. They are used on what is called open cir- 
cuit work, i.e., for intermittent service, as telegraph, telephone, 
or call-bell service. Dry cells are all of this type. Innumerable 
forms of cells have been used, which must be studied in special 
works. Such as do not first require the action of an electric 
current to put them into condition for producing a current are 
called primary cells. 

Experiment No. 88, page 305. — Polarization and depolarization. 
In the Weston Normal Cell, one pole is of pure mercury covered with 
a paste of mercurous sulphate. On this lie crystals of cadmium sulphate 
which are covered by a saturated solution of cadmium sulphate. The 
other pole is cadmium amalgam covered by crystals of cadmium sulphate 
and those by saturated solution of cadmium sulphate. The internal re- 
sistance of such a cell is about 900 ohms. Its E.M.F. at 20 C. is 1.0183 volts 
and at any temperature, t, is given by the equation 

Et = E>o — 0.0000406(7 — 20) — 0.00000095 (/ — 20) 2 + 0.0000000 1 (t — 20). 3 
As a standard of E.M.F. this has taken the place of the Clark cell men- 
tioned in Art. 188. The volt, then may be defined as the jgog g- part of 
the E.M.F. of the Weston Normal Cell, at 20 C. 

217. The Storage or Secondary Battery. — It was pointed 
out (Art. 215) that an electrolytic cell becomes a source of 
current on its own account after it has been in action. If a 
cell is made by putting into dilute sulphuric acid two lead 
plates that are coated with lead peroxide, the coating becomes 
a paste of lead sulphate. If a current is passed through this 
cell one plate, by loss of oxygen, becomes covered with pure 



284 POTENTIAL; MAGNETISM; ELECTRICITY 

spongy lead, and the other is coated with lead peroxide. These 
have a high difference of potential, and, moroever, their condi- 
tion chemically is unstable. A continuance of the charging 
will finally produce a difference of potential of about 2.5 
volts between the terminals, and chemical energy will have 
been expended to a definite amount in charging the cell. If, 
now, the source of the charging current is disconnected, the 
storage cell is in condition for use. Connecting its terminals 
to form an external circuit, reverse chemical action occurs in 
the cell, and a current is produced which will continue until the 
energy of the inverse chemical action has been expended electri- 
cally. Various other forms of secondary batteries have been 
devised. 

The electromotive force of any cell rises to an amount that is 
determined, not by the amount, but by the kind of chemical re- 
actions that go with it. The E.M.F. of any cell, then, is deter- 
mined by the nature of the materials that compose it and not 
in any degree by their quantity or size. 

218. Joining Cells to Form a Battery. — Properly speaking, 
one combination of plates and liquid constitutes a cell or an ele- 
ment; a battery is a combination of two or more cells, though in 
careless speech it is not uncommon to call a single cell a battery. 
When several cells are joined with the positive pole of one to the 
negative of the next, successively, they are said to be joined 
tandem or in series; the E.M.F. of the combination is the sum 
of them all, and the battery resistance is increased in the same 
way. When the positive poles are joined together they have 
a common potential, and so will the negative poles if so joined, 
and when so connected they are said to be joined parallel, or in 
multiple. The E.M.F. of the combination then is the same as 
that of a single cell, and if n such cells are thus joined, the in- 
ternal resistance becomes - part of that of a single cell. It 

may be shown that the maximum current from a voltaic bat- 
tery will be produced when the cells are so combined that the 
total external resistance equals the total internal resistance. 



DISPLACEMENT CURRENTS 285 

219. Displacement Currents. — (See Watson, Art. 577 and 
Arts. 585-595, also Glazebrook's Electricity and Magnetism, 
Art. 255.) 

When two plates are separated by a dielectric, as A, B 
(Fig. 125), they constitute a condenser and may be brought 
to a high difference of potential by being charged from a 
source of E.M.F., as at E. The effect of E in charging the 
plates has been regarded as a displacing of positive electricity 
in the direction of the current through the dielectric, and of 
negative electricity in the opposite direction, and this displace- 
ment evokes a condition of strain in the dielectric. This 
strained condition may rise to the extent of overcoming the 
ability of the dielectric to withstand it, and discharge the 
condenser across the dielectric from A to B. Without going 
so far as that, however, 



Fig. 125. Displacement Currents. 



if E is replaced by a con- 
tinuous conductor from A a 
to B, or even if there is g< — — >h 
a small gap there, occu- 
pied by a dielectric that 
is not able to withstand 
the difference of potential 
between A and B, then the condenser will discharge suddenly 
through AEB. This is the way a Leyden jar is discharged by 
means of a discharger. Instead of the discharge being final 
in a single action, however, it is found that B rises to a higher 
potential than A as if the electricity had possessed inertia, 
and this is followed by a surging back of the discharge from 
B to A through BE A, a process which is repeated thousands of 
times in the small fraction of a second that is occupied in the 
apparent discharge of the condenser. This oscillatory discharge 
is accompanied by corresponding alternations of stress in the 
dielectric between A and B, and also in that at E if there be one 
there. These alternations of stress in the dielectric are ascribed 
to what Maxwell has termed " displacement currents." Every 
such alternation of stress between A and B due to a displacement 



286 POTENTIAL; MAGNETISM; ELECTRICITY 

current, no matter how brief, is extended outward through the 
ether of space in the form of electric waves at right angles to the 
direction of the displacement current, much as water waves 
would move out from a vertical rod that is moved up and down 
through the surface of the water. Not only so, but as every elec- 
tric current has a magnetic field of force represented by lines of 
force encircling it, in the figure, if displacement currents pass 
between A and B, electric waves move out toward G and H, and 
at G and H there will be magnetic force perpendicular to the 
plane of the paper, and alternating in direction. These last 
alternations are electromagnetic waves which traverse space 
simultaneously with the electric waves and always have a direc- 
tion at right angles to them. 

220. Wireless Telegraphy. — The electric waves discussed in 
the preceding article are the means of wireless signaling through 
space. The essential principles are as follows: 

At the transmitter, oscillations are set up in a local circuit 
containing a condenser, by the passage of sparks between two 
metal terminals, forming a spark gap, which connect with the 
high-potential winding of an induction coil or a transformer. 
These oscillations are usually transferred inductively to another 
circuit which extends from the ground to a series of parallel 
wires suspended in the air and called an "antenna" or "aerial." 
When the induction coil is operated by closing a key in its pri- 
mary circuit, electric waves depart from the antenna, which have 
a definite frequency or wave length depending on the capacity 
and inductance of the two circuits at the transmitting station. 
In sending messages, the key is manipulated in accordance with 
a telegraph code, and the electric waves are sent broadcast in 
groups corresponding to dots and dashes. 

To perceive these waves at a receiving station, requires an 
antenna associated with some form of "detector", usually of the 
crystal or audion type. A telephone receiver forms a part of the 
detector circuit, so that the action of the electric waves on the 
detector can be heard, and the signals interpreted. 

To be most effective the receiving antenna circuit should be 
attuned to the wave length of the transmitting station with 



DISCHARGE OF ELECTRICITY THROUGH GASES 



287 



Oo 




which it is working. (Compare Art. 139 on resonance of air 
waves.) A complete receiver, therefore, includes coils and con- 
densers which can be varied so as to tune the receiver to any de- 
sired transmitter. The waves used in radio communication have 
wave lengths from 150 to 10,000 meters. 

Fig. 126 shows a typical circuit arrangement of a trans- 
mitting station at (a) and of a receiving station at (b). In the 
former, the condenser C is charged from the transformer or 
induction coil B on 
closing the key K. 
Thereupon the con- 
denser discharges 
through the gap cir- 
cuit CDG, setting 
up high-frequency 
oscillations. These 
chargings and dis- ^ Fig. 126. (6) 

chargings occur many times during the depression of the key, 
the number depending upon the vibration rate of the vibrator in 
the case of the induction coil or on the frequency of the alter- 
nating current supply in the case of the transformer. The 
oscillations are communicated by induction to the antenna cir- 
cuit AFE which sends out the electric waves. 

When the waves impinge upon the receiving aerial AMLE' ' , 
Fig. 126 (b), they set up an alternating E.M.F. which induces a 
high-frequency alternating current in the circuit S-C. Shunted 
around condenser C is the crystal detector D and "stopping 
condenser" S'. Due to the unilateral conductivity of the crystal 
detector, only a pulsating direct current is permitted to flow, 
which builds up a charge on the stopping condenser. This 
condenser then discharges through the telephone receivers T, 
rendering the impulse audible. By adjusting the point of contact 
of L with M the circuit is attuned to the waves received by A. 

221. Discharge of Electricity through Gases. — If two metal 
conductors are separated by a gas, a high difference of potential 
is necessary to overcome the resistance of the dielectric between 
them for a gap of a few centimeters. The necessary potential 



288 POTENTIAL; MAGNETISM; ELECTRICITY 

difference depends somewhat upon the form of the terminals be- 
tween which the discharge occurs, but with the ends of the second- 
ary of an induction coil separated by one centimeter of air that 
has not been electrified, a difference of potential of from 10,000 
to 30,000 volts is necessary to cause a spark discharge across the 
opening. For distances greater than 10 cm., the voltage required 
before a spark will pass, is given approximately by the equation 

V = 4800^+24,000, 
where d is centimeters and V is the maximum difference of 
potential in volts. (See Art. 167, Note.) 

If the gas through which the discharge occurs is inclosed in a 
tube, into which lead the terminals of an induction coil or an 
electrostatic machine, and the tube can be connected with an 
air pump, so that the gas can be extracted and a more or less 
perfect vacuum formed, the electric discharge between the ter- 
minals undergoes remarkable changes in character as the pressure 
is reduced. 

If the apparatus is capable of producing a spark of, say, 10 cm. 
in open air, and the terminals in the tube are, say, 20 cm. apart, 
there will at first be no discharge in the tube when the coil is set 
in operation. As the pressure is reduced there will presently 
appear between the electrodes a thin quivering streak of light 
surrounded by a violet sheath; with further diminution of pres- 
sure to, say, 2 mm. of mercury, the tube is filled with a diffused 
violet light, and when the pressure is as low as one millimeter this 
light breaks up into laminae or striae in planes perpendicular to 
the line of discharge between the electrodes. The tube of gas 
in this condition is known as a Geissler tube. A much smaller 
potential difference here will produce the discharge. A potential 
that will bridge a gap of four or five millimeters in air will produce 
a discharge through a Geissler tube of 20 cm. or more. Such 
tubes are prepared with various gases in them, for the purpose of 
studying the light that is peculiar to each gas on its own account. 
In a Geissler tube the line of discharge follows the shape of 
the tube from one electrode to the other, whatever may be the 
number or variety of turns it may have. 



DISCHARGE OF ELECTRICITY THROUGH GASES 289 

As the vacuum is made more complete, say, to a pressure as low 
as one-thousandth of a millimeter, the gas is so rarefied that the 
average distance traversed by the molecules between impacts is 
comparable to the dimensions of the bulb or tube containing the 
gas. This is the condition described in Art. 95 (1) as a " Crookes' 
layer," and the tube or bulb is called a Crookes' tube. When this 
state is reached, the potential difference required for the electric 
discharge between the terminals within the tube is much greater 
than in the Geissler tube. The discharge from the negative 
terminal, or the cathode, now displays new peculiarities. It is 
said to consist of " cathode rays." These comprise electrified 
particles of the rarefied gas, and also an order of radiation from 
the surface of the cathode itself, all in straight lines normal to 
the surface. The rays carry energy, and where they strike 
upon the walls of the tube, or upon material within the tube, they 
heat it, or they produce chemical or mechanical effects. 

If the cathode is a concave disk the rays may be focused from 
it and thus the energy be concentrated. The rays will not fol- 
low the shape of the tube, but they may be deflected from a 
straight path by a magnet. Among their most striking proper- 
ties is that of causing certain substances to fluoresce; i.e., when 
they are directed upon glass, or certain minerals, they cause 
those substances to emit a light of their own. To a slight extent 
the special cathode rays (not the electrified gas) penetrate the 
walls of the tube or even a thin sheet of metal, as aluminum. 

Illustrations. — Geissler tubes and Crookes' tubes. 

The cathode rays are now regarded as minute, negatively elec- 
trified particles, moving with great velocity, comparable to the 
velocity of light.* They are called ions, though such an ion 
differs in mass and velocity from the ion of electrolysis. A gas 
is not ordinarily a conductor of electricity, but any gas upon 
which cathode rays are directed acquires the power to conduct 
electricity, its particles becoming themselves so electrified that 

* The velocity varies with the square root of the potential difference, and is 
about ^o.that of light, or 10,000,000 meters/sec. with a PD = 300 volts. 



290 POTENTIAL; MAGNETISM; ELECTRICITY 

in their freedom of movement they will carry away a charge from 
a statically electrified body, or facilitate the discharge between 
two electrodes. This power may be conferred upon gases by 
other means as well as by cathode rays, but whenever a gas is 
thus made conducting, it is said to be ionized. 

From elaborate investigations, notably by Prof. J. J. Thom- 
son, of Cambridge University, England, and later by many other 
distinguished physicists both in Europe and America, the theory 
results that the electric charge, e, carried by a hydrogen ion 
(cation) in electrolysis is equal to that on an ion discharged from 
the cathode in a rarefied gas, but that the mass of the latter 
particle is only about one eighteen-hundredth as great as the 
mass of the hydrogen ion. Professor Thomson called this minute 
particle a corpuscle, but it is now termed an electron, the name 
ion being more commonly applied to the carrier of electricity in 
electrolysis. 



e 



Note. — See Art. 213. For the hydrogen ion the ratio of quantity to mass, 
= 9647, where e is electromagnetic units, and m is grams. For cathode ray 

rn 

e 
particles the corresponding ratio has been found to be — = 1.772 X io 7 . If e 

m 

is the same in both instances, i.e., if the charge on a hydrogen ion in electrolysis 

equals that on a cathode-ray particle, the mass of the hydrogen ion must be 

1.772 X io 7 

times that of the gaseous ion, or the mass of the hydrogen ion 

9647 ^ 

is 1840 times the mass of the electron. 

222. Rontgen (or) X Rays. — When cathode rays strike upon 
bodies these bodies emit a species of radiation known as Rontgen 
rays, from their discoverer, Professor Rontgen, or as X rays as he 
himself termed it. While the nature of X rays is not certainly 
known it is pretty certain that they are not material particles 
like those constituting cathode rays. They are probably wave 
motion of extreme rapidity, set up in the ether by the impact of 
cathode particles, and proceeding from the surface of impact. 
In a Crookes' tube this would mean that the X rays proceed from 
the walls of the tube; or if the cathode rays are concentrated upon 
any special part of the tube or upon the body within the tube, then 



RONTGEN (OR) X RAYS 



291 



that part or body becomes the source of X rays. In the com- 
monest form of tube for X-ray service, the anode either is a small 
sheet of platinum inclined at about 45 ° to the line of discharge 
between the electrodes, or it is directly connected to it, and the 
cathode is of aluminum, cup-shaped, which brings the cathode 
rays to a focus upon the platinum anode. The latter then emits 
X rays (see Fig. 127). X rays, like cathode rays, cause strong 
fluorescence, but penetrate many substances that are impervious 




Fig. 127. An X-ray Tube. 

to the cathode rays. They also produce strong photographic 
action, and they ionize gases. They penetrate glass with con- 
siderable readiness but are intercepted by metals, while various 
organic substances vary in the degree to which they permit pas- 
sage through them. In the tube of Fig. 127, the X rays are 
emitted from one side of a plate, upon which the cathode rays 
from the cup-shaped terminal of the cathode a impinge, and pro- 
ceed in all directions on that side, so that the portion of the 
glass bulb on that side of the plate fluoresces a rich green or blue, 
while the other part is unexcited and remains dark. The action 
by which objects may be viewed by means of X rays is not at all 
like that by which light makes objects visible. Usually a screen 
of cardboard coated with a fine layer of some fluorescent sub- 
stance, as tungstate of calcium, for example, forms one end of a 



292 POTENTIAL; MAGNETISM; ELECTRICITY 

dark box into which the eye can look while all light is excluded. 
The fluorescent surface is on the inside. When X rays, pene- 
trating the cardboard, fall upon the mineral coating within, the 
inner surface becomes luminous as an effect of the X rays, and 
the light from that surface is not X rays but common light. If 
an object, as the hand, is placed against the outside of the screen, 
it intercepts in some measure the X rays; the flesh permits the 
rays to pass through without much hindrance and therefore to 
cause slightly diminished fluorescence; the bones are more im- 
pervious, and consequently the part of the screen covered by 
them is sheltered and the intercepting object looks dark; thus 
this shadow picture reveals the bones dark, in a hazy envelope of 
lighter tissue, upon a still brighter field. The box for viewing 
it is a fluoroscope. (Exhibit X rays.) 

223. Radioactivity. — From the mineral pitchblende have 
been derived several compounds, notably salts of the metals 
uranium, thorium, and more recently radium, which emit a 
species of radiation that possesses many of the properties of 
cathode rays. The most striking effects are photographic action, 
the causing of fluorescence, and especially the ionization of gases. 
The power of giving out rays that ionize gases is called radio- 
activity. The rays from radioactive bodies are separable into 
three kinds called respectively a rays, /3 rays and 7 rays, each of 
which has properties peculiar to itself. 

The more intensely radioactive substances, notably radium, 
are continually giving off material, termed vaguely an " emana- 
tion," which is itself like a radioactive gas, and which, after a 
time, becomes helium. The energy of radiation is great, and as 
the radiation seems to proceed from within the substances the 
bodies emitting it are affected by its passage so as to be kept at 
a temperature several degrees higher than that of the atmosphere 
around them. In the course of the transmutation which the 
substances undergo, they liberate an enormous supply of energy. 
Special works on the subject are Radioactivity, by E. Rutherford, 
Conduction of Electricity through Gases and Radio- Activity, by R. K. 
McClung,— Blakiston& Co., Philadelphia; and Chapter XV of The 



ELECTRON THEORY OF ELECTRICITY 293 

Electron Theory, by Fournier, — Longmans, Green and Com- 
pany. 

Professor Crookes devised an instrument by which the fluores- 
cent effect of the radiation from radium is beautifully shown. 
E It is called a spinthariscope. By an eye 

piece E (Fig. 128), in one end of a short 
metal tube, is viewed a small screen of 
paper S, coated with zinc sulphide. Close 
above 5 is a small strip of metal, the head 
M of which has been dipped into a solu- 
tion of radium bromide, and is thus coated 
with a minute quantity of this radioactive 
substance, which remains on the metal 



— ^ — 



Fig. 128. The Spinthari- a fter it is dry. The radiation from it 
3Cope ' causes the zinc sulphide to scintillate with 

constantly changing, intermittent flashes of points of light, due 
to the bombardment by the particles emitted from M. 

224. Electron Theory of Electricity. — (An interesting state- 
ment of both theory and experimental facts concerning electrons 
is given by J. A. Fleming in Popular Science Monthly for May, 
1902; also see The Electron Theory, by Fournier, — Longmans, 
Green and Company.) The theory is summarized as follows, 
by Professor Glazebrook (Glazebrook's Electricity and Magnetism, 
Art. 270): " According to the electron theory a neutral atom 
consists of an electron or series of electrons each carrying its 
negative charge together with a positively charged nucleus, the 
total positive charge being equal to the sum of the negative 
charges on the electrons. 

"It is possible in various ways to attach one or more elec- 
trons to such an atom; it then becomes negatively charged; it 
is also by hypothesis possible to detach one or more electrons, the 
remainder — the coelectron as Professor Fleming has called it — 
remains positively electrified. 

" A univalent atom, like hydrogen, is one which can receive or 
give up one electron and no more. A divalent atom can receive 
or give up two electrons, and so on. 



294 POTENTIAL; MAGNETISM; ELECTRICITY 

"A current of electricity is a stream of electrons; a body 
through which the electrons pass freely is a conductor; within a 
nonconductor they cannot move about readily. A gas may be 
nonconducting; because of the absence of electrons; if they are 
introduced it gains conductivity. All the phenomena of electric 
discharge and current are convection phenomena. 

" When electromotive force is applied to a conductor, the 
electrons are urged through the conductor; if it be a gas at 
low pressure they stream from the cathode as the cathode 
rays. 

"In an electrolyte in solution, some of the free ions are posi- 
tive; they are coelectrons, and the electrons which have left 
them have joined on to other ions, making them negative; there 
is probably a continual interchange going on, but on the aver- 
age the above statement represents the position. 

" The negative ions are driven by the E.M.F. to the anode, 
the positive ions travel to the cathode. 

"In a solid conductor the same kind of separation and combi- 
nation of ions and electrons is taking place, but the ions are not 
free to move; the current is conveyed by the electrons moving 
on from ion to ion through the solid ; the solid is porous to them 
but not to the ions." 

If the quantity of electricity constituting the charge upon an 

ion is called e and the mass of the electron m, the ratio of — 

m 

for an electron is about eighteen hundred times as great as 
for a hydrogen ion in electrolysis, and if the charge e may be 
assumed to be alike in both ions, it follows that the mass of an 
electron is only about one eighteen-hundredth that of a hydro- 
gen ion. The actual amount of the elemental charge e has 
been determined by various methods with fairly consistent 
results. Among other important conclusions, these give for 
accepted values at present, £ = 4.7 Xio -10 electrostatic units, 
this would equal 4.7Xio _10 -^(3Xio 10 ) or 1.57 Xio -20 electro- 
magnetic units. The number of molecules in one cubic centi- 
meter of gas at o° C. and 76 cm. pressure is 2750 Xio 19 ; the 



ELECTRIC ACTIONS SUMMARIZED 295 

number of molecules in a gram molecule* is 6.16 Xio 23 ; the 
kinetic energy of agitation in ergs of a molecule at o° C., 76 cm. 
pressure is 5.57 Xio -14 ; the mass in grams of an atom (half a 
molecule) of hydrogen is 1.63 Xio -24 . See Kaye and Laby's 
Tables, pp. 97, 98. 

225. Electric Actions Summarized. — In our survey of current 
electricity we have come to recognize 
As sources of electromotive force, 

Friction or cleavage. 

Motion of a conductor in a magnetic field. 

Contact of different substances. 

Chemical Combination. 

Heat. 
As effects of currents, 

Heat. 

Magnetization. 

Attraction and repulsion of conductors. 

Chemical decomposition. 

Secondary effects of cathodic discharge. 
As the nature of a current, the transfer of electrification, which 
may be the 

Propagation of a strain (or relaxation) through the ether 
of space or of a dielectric; or 

The travel of electrons through solids, liquids and gases. 

*A gram molecule is the weight of gas whose volume at o°, 76 cm. is 22,400 
c.c; i.e., the volume of 32 g. of oxygen. Molecular weight is the weight in grams 
of a gram molecule; i.e., it is 2.016 grams multiplied by density of the gas com- 
pared to hydrogen. For hydrogen it is 2.016; for oxygen it is 2.016 X 15.88 (= 32). 
In round numbers it is usual to take density of hydrogen, 1; of oxygen, 16; molec- 
ular weight of hydrogen, 2; of oxygen, 32. 



EXPERIMENTS TO ILLUSTRATE CHAPTER V. 

Experiment No. 67, Art. ij6. Formation of Magnetic Lines of Force. 

Place a pane of dry glass over one or more magnets, bar or horseshoe, 
and sprinkle over the glass dry, fine iron filings by sifting them through a 
piece of gauze. On tapping or jarring the glass the particles of iron arrange 
themselves along lines of force in the plane of the glass. Project upon the 
screen. 

Experiment No. 68, Art. 156. Law of Magnetic Force. 

NS (Fig. 129) is a long powerful magnet, placed horizontally at right 
angles to the plane of the magnetic meridian, and ns a magnetic needle with 

its pole, say, 30 cm. from 
n s N S the opposite pole of NS. 

~ ' If ns is slightly deflected 

and released it will oscil- 
late with a period due to 
the force of N, the direc- 
tion of which is in the 



Fig. 129. 



line of the two magnets. The conditions of oscillation of ns are similar to 
those of a pendulum under the force of gravity. For such a pendulum it 
was seen, Art. 26, that the time of oscillation varies inversely as the square 
root of the force. Observe the period T of oscillation of ns with N at 
various distances d from s. It is found that T oc d. If the force is F, by 

the law of the pendulum, Toe — -■ 

VF 

Therefore — - ocd- or VFoc-, 

Vf d 

or Fao±' Q.E.D. 

d 2 

Experiment No. 6g, Art. 159. Induction in Earth's Magnetic Field. 

Hold an iron rod AB (Fig. 130), 70 or 80 cm. long and 10 to 15 mm. 
thick, in an east and west position opposite the center of the compass needle 
ns, at a distance of about 10 cm. If AB is not magnetized it will cause no 
deflection of ns. Turn it into a position parallel to ns, B to the north; .4 
will now be found to attract n and repel s, showing that it is a south pole. 
Move BA along horizontally until B is in the place of A, and its north 

296 



EXPERIMENTS 



297 



AB has 
If it is 




Fig. 130. 



polarity will be evidenced by its attraction of s and repulsion of n, 
become magnetized by induction in the earth's magnetic field 
struck two or three times sharply by n 

a hammer while in the north and 
south position, the magnetism is con- 
siderably heightened. 

Now place the bar in a vertical 
position, B downward and again 
give it a few sharp taps in this posi- 
tion. While held vertically the end 
A will now show a much stronger at- 
traction of n and repulsion of s, and 
when the bar is moved up until B is 
opposite the center of ns, the reverse 
polarity is strongly shown. This indicates that the vertical component 
of the earth's magnetism is stronger than the horizontal. Finally, the 
strongest magnetization is obtained by holding the bar in the plane of the 
magnetic meridian, and dipping downward at an angle of about 70 below 

the horizontal (at New York), i.e., in the 
direction of the earth's magnetic lines of 
force. 

With a lantern arranged for vertical pro- 
jection, ns may be projected on the screen, 
f/ / II \ \\ an< ^ ^ e m ^ uence °f tne magnetism induced 

I I s/\ 1 1 \ in AB shown on a large scale 

Experiment No. 70, Art. 164. {Nos. 70 to 

72, inch, illustrate Electrification by 

Induction.) 

Rub a piece of sealing wax with wool or 
fur, and bring it near the knob of a gold 
leaf electroscope (Fig. 131). Negative elec- 
trification is driven to the gold leaves which 
diverge in consequence of their repulsion for 
each other. While they are thus divergent, 
owing to the proximity of the sealing wax, 
touch the knob of the electroscope with the finger. The negative charge 
escapes while the positive electrification is held by the presence of the nega- 
tive sealing wax, and the leaves collapse. Take away the finger and then 
remove the sealing wax; the positive charge distributes itself over the leaves 
as well as the knob and the leaves diverge with a positive charge. On the 
approach of a negatively electrified body to the electroscope the leaves sink 




Fig. 131. 



The Gold Leaf Elec- 
troscope. 



298 



POTENTIAL; MAGNETISM; ELECTRICITY 



together, but the approach of a positively charged body causes them to 
separate further. 

Experiment No. 71, Art. 164. 

A striking example of electrical induction is shown in the electrification cf 

a water jet. 

Arrange a small nozzle, as A (Fig. 132), so as to give a jet of water slightly 

inclined to the vertical. If the water pressure in the lecture room is suffi- 
cient, the tube T may be 
connected to a faucet at 
the lecture table; other- 
wise it may be used as a 
siphon from the vessel V, 
mounted upon a stand. 

The jet separates into 
drops a short distance 
above A. If an excited 
rod, say of sealing wax, 
is brought close to A , the 
jet breaks into a broad, 
fine spray; but if the rod 




Fig. 132. Electrification of a Water Jet. 



is very feebly excited, or is held a couple of meters beyond the falling drops, 
they coalesce and form a more compact stream. 

In the first case, negative electricity is repelled to earth or to V, and the 
jet at A is electrified positively before breaking into drops, and these drops 
repel one another. In the second case, the falling drops are all charged posi- 
tively on the side next to the sealing wax and negatively on the farther side, 
and they attract one another, besides having their rotary motion checked. 

If the spray falls upon an insulated metal plate, as, e.g., the cover of the 
electrophorus, the plate becomes charged, and on presenting it to the electro- 
scope, as in the preceding experiment, its charge is found to be of the opposite 
character to that of the excited rod. On the other hand, if a wire is led from 
the water in V to the knob of the electroscope it gives the latter an electrifica- 
tion of the same sort as that of the rod. Except for this last test, it is well 
to connect the water in V by a wire to the earth. 

Experiment No. 72, Art. 164. 

A thin cake of sealing wax or hard rubber, w (Fig. 133), in a shallow metal 
case c, is supported by an insulating stand S. A cover plate p of thin metal, 
e.g., tin plate, a little smaller than w has an insulating handle S'. c should be 
put in connection with the earth. With p removed, electrify w by rubbing 
with cat's fur; place p upon w; positive charge is induced on lower side 
of p and negative on upper; discharge latter by touching p with the finger. 



EXPERIMENTS 



299 



By means of the handled remove p; it is charged positively and when 
brought near the hand or any other body, it communicates its positive charge 
with a slight spark, p may then be re- 
placed on w and the operation repeated. 

Experiment No. 73, Art. 175. Static 
Electrification from Voltaic Battery. 

The plates of a condensing electro- 
scope are insulated from each other by 
a coat of shellac varnish on the surfaces 
next each other. If the other surfaces 
are not thus varnished, they are con- 
ducting and may be charged by contact 
with another charged body. Touch the 
top of the upper plate with the end of 
an insulated wire from one pole of a vol- 
taic battery, and the under surface of 
the lower plate with a wire from the 
other pole of the battery. The plates 
acquire a charge, their potential differ- 
ence being that of the battery terminals. 
The quantity in the charge may be con- 
siderable but no effect is seen in the gold leaves, 
and the leaves diverge 




Fig. 133. The Electrophorus. 



Remove the upper plate 
The charge may now be tested as to whether it is 
positive or negative by bringing near the electroscope an excited rod of 
glass or sealing wax. The electrification from the battery is identical in 
character with that from friction. The effect is perceptible in a charge 

from a battery of as lit- 
tle as five or six volts. 
The experiment may 
readily be projected on 
the screen. 



v*§§5^2 



Experiment No. 74, Art. 
180. To show the mag- 
netic field around a 
current. 



Fig. 134- 



Magnetic Lines of Force Produced by an 
Electric Current. 



Drill a small hole in a 
pane of glass as at O 
(Fig. 134), and perpen- 
dicularly through this lead a wire about No. 16 or 18 in size, that is part of 
an electric circuit. Pass a current of 8 or 10 amperes through the wire and 



3°° 



POTENTIAL; MAGNETISM; ELECTRICITY 



sprinkle iron filings on the glass. On tapping the latter the filings will 
arrange themselves in circular whorls around the wire. Project on the screen. 

Experiment No. 75, Art. 180. Oersted's Experiment. 

Suspend a slender magnetic needle and let it come to rest in the mag- 
netic meridian. If a straight portion of a wire carrying a current is held in 
a parallel direction above the needle the latter is deflected; if the current 
is placed below the needle the deflection is in the opposite direction. 

Experiment No. 76, Art. 189. Conductivity of a Liquid. 

Solder a disk of sheet copper, as A or B (Fig. 135), about 3 cm. in diam- 
eter, to the end of each of two insulated wires, and place the wires in a tall 

glass vessel about 4 cm. in diam- 
eter, e.g., a graduate glass. Con- 
nect the terminals C and D so as 
to complete a circuit through an 
electric bell and two battery cells. 
Fill the jar with water. Its con- 
ductivity is poor and little or no 
current flows. Add a few cubic 
centimeters of sulphuric acid, and 
the resistance of the water is so 
greatly reduced that the bell rings. 
By raising or lowering one of the 
electrodes, as A, the variation in 
the current shows the variation of 
the resistance of the water column 
with change of length. 

By using other liquids in the 
jar, some idea is obtained of their 
various conductivities. 

Experiment No. 77, Art. 199. Localization of Energy in a Conductor. 

Connect in series three or four links of thin platinum wire (about No. 30), 
4 or 5 cm. in length, alternately with similar links of bare copper wire, and 
through the chain pass a current of 5 to 10 amperes, controlled by a rheostat. 
The same current traverses the copper and the platinum links, but, owing 
to the greater resistance of the latter, they glow and become white hot while 
the copper remains dark. 

Experiment No. 78, Art. 199. 

Through a rheostat connect a No. 26 or 28 iron wire, about 150 cms. long, 
with the terminals of the no-volt electric light system, and apply the 




EXPERIMENTS 



301 




current to heat the wire. Gradually increase the current until the metal is 
white hot. Owing to its expansion by heat the wire sags at the middle as 
much as 12 cm. From this sag the elongation of the wire may be deter- 
mined, and from the coefficient of ex- 
pansion an approximate value of the 
temperature may be computed, 1200 C. 
to 1500 C. 

Experiment No. yg, Art. 201. {Nos. 
yg and 80 show Attraction and 
Repulsion of Currents.) 
Roget's Spiral (Fig. 136) is a coil of 
30 or 40 turns of copper wire suspended 
so that its lower end just touches the 
surface of mercury in a cup. The mer- 
cury and the upper end of the coil are 
in circuit with a battery. The end thus 
in contact with the mercury should be 
a tip of platinum wire attached to the 
copper. The spires should be about 4 
cm. in diameter and about 2 mm. apart. 
With an E.M.F. of 8 or 10 volts a 
strong current will traverse the wire, 
and the attraction of the parallel turns will cause a shortening of the coil 
and a break in the circuit at the mercury surface. Then the coil elongates,. 

contact is again closed, the current is re- 
fins' stored and the process is repeated and 
continued in a steady vertical oscillation 
of the coil. 

Experiment No. 80, Art. 201. 

Two wires a meter or more in length 
(Fig. 137) suspended from binding posts 
at a distance from each other of 1 or 
2 cm., dip into a cup of mercury at their 
lower end. If the binding posts are con- 
nected to the terminals of a battery of, 
say, 10 or 12 volts, the currents in the 

two wires are in opposite directions, and the wires separate by repulsion. 
If the binding posts are connected to each other and one terminal of the 

battery is connected to them and the other to the mercury, the currents 

through both wires are in the same direction and the wires move up closer 

to each other by attraction. 



Fig. 136. Roget's Spiral. 




Fig. 137. 



3 02 



POTENTIAL; MAGNETISM; ELECTRICITY 



If the wires hang in the light of the lantern, some distance from the screen, 
their shadows on the screen, and the attraction and repulsion, may be more 
easily observed throughout the room. 

Experiment No. 81, Art. 202, 

Currents due to electromagnetic induction may be shown by turning a 
coil in a field no stronger than that of the earth. Use a spool of many turns, 
several thousand, of fine wire. (The secondary of a small induction coil 
may be used.) Attach the ends of the wire to a sensitive galvanometer 
(preferably a D'Arsonval in which a beam of light reflected from the mirror 
is focused on a scale). Holding the coil with its axis parallel to the earth's 
magnetic lines of force, suddenly invert it. During the turning a current is 
instituted, as shown by the deflection of the spot of light. When the coil 
is suddenly reversed to its first position the light is deflected in the opposite 
direction. By numerous repetitions, timing the alternating motion of the 

coil with the movement of 
the light, the swing of the 
latter may be made very 
large. The effect is height- 
ened by placing an iron core 
in the spool. 

Instead of induction from 
the earth's field, let the coil 
remain stationary in any po- 
sition, and suddenly insert a 
bar magnet in it; a current 
(a) is momentarily produced. 

Suddenly drawing the mag- 
net out of the coil induces 
a current in the opposite 
direction. 

Experiment No. 82, Art. 204. 

The magnetic field of a 

circular conductor (Fig. 

138(a)), or of a solenoid 

(Fig. 138(6) ), may be shown 

by winding a wire spirally 

several turns, 5 or 6 mm. 

apart and about 2 cm. in 

diameter, through punctures 

in a piece of mica. On passing a current of 8 or 10 amperes through this 

coil and sprinkling iron filings upon the plate, the lines of force are at once 





Fig. 138. Magnetic Field of Force within a 
Coiled Conductor. 



EXPERIMENTS 303 

seen. With vertical projection apparatus this and similar experiments may- 
be shown on the screen. 

Experiment No. 83, Art. 206. Self- Induction. 

Connect a wire to one pole of a battery of 10 or 12 volts, and touch the 
free end momentarily to the other pole; on suddenly separating them a 
spark ensues. If now the end of the wire is connected to a rough metal 
surface, say, a coarse file, and the current is led by the other terminal through 
a coil of several hundred turns of insulated copper wire, about No. 18, wound 
upon a lead pencil, and the free end of this coil is drawn along the file, the 
flashes resulting from the breaks of contact are more intense than before; 
if the pencil core of the coil is replaced by a corresponding piece of iron the 
effect is still further heightened, and the sparks emitted on drawing the 
end of the wire along the file are white. 

Instead of a specially wound coil, the primary of a small induction coil 
may be used. 

Experiment No. 84, Art. 208. Cycle of Energy Changes. 

If the commercial current at no volts, an electric motor of as much as 
\ H.P., and a small dynamo capable of generating 30 volts or more are 
available, it is an instructive experiment to couple the motor to the dynamo, 
and from the latter to operate a small arc light, and then trace the complete 
cycle of energy changes, as, e.g.: 

Energy of Light (of the sun) ages ago produced luxuriant vegetation 
that afterwards formed beds of coal; energy of chemical separation, trans- 
formed into heat by combustion of coal in the furnaces under steam boilers ; 
heat, transformed into energy of gas (steam) in the boilers; energy of steam, 
transformed into mechanical energy of steam engine operating dynamos in 
power house; mechanical energy of steam engine, transformed into electrical 
energy of dynamos supplying current; this electrical energy, transmitted 
along the mains, transformed into mechanical energy in the electric motor 
in the lecture room; this mechanical energy again transformed into electrical 
energy in the small dynamo, and this electrical energy again transformed 
into that of Light (of the arc). 

Experiment No. 85, Art. 212. Thermoelectric Current. 

Cut a strip of sheet lead 1 cm. wide and 30 cm. long, scrape one end 
bright and hammer into the bright lead a similarly cleaned end of an iron 
wire, making an intimate junction of lead and iron. From the other ends of 
the lead and the iron complete a circuit by any kind of wire through a sensitive 
galvanometer. If the junction of lead and iron is warmed simply by hold- 
ing it between the thumb and finger, a current through the circuit will be 



3°4 



POTENTIAL; MAGNETISM; ELECTRICITY 



indicated by a slight deflection of the galvanometer needle or spot of light, 
and this will much increase if the flame of a match or burner is applied 
to the junction. 

Experiment No. 86, Art. 213. 

The electrolysis of water is shown by means of an apparatus like that of 
Fig. 139. The two tubes are filled with water to which has been added a 
little sulphuric acid to- give it conductivity. An elec- 
tromotive force of over 2.5 volts is needed from a bat- 
tery in circuit with the binding posts at the base. 

With platinum electrodes both dipping into a flat- 
sided glass vessel of acidulated water, and the latter 
mounted on the stand of the lantern, the process of 
electrolysis and the liberation of gas at each electrode 
may be projected upon the screen. 

Experiment No. 87, Art. 213. Lines of Flow in a 
Current Sheet. 

A sheet of coarse filter paper or absorbent paper, 
about 10 cm. by 15 cm., moistened with a solution of 
zinc sulphate, is laid on a pane of glass and fine zinc 
filings are sprinkled over it. 

The terminals of an ordinary electric lighting circuit 
are applied to the sheet thus prepared, 10 or 15 cm. 





Fig. 139. Apparatus 
for Decomposition 
of Water. 

apart, and an elec- 
tric current passes as 
from A to B (Fig. 
140). 

Lines of dark me- 
tallic zinc grow by 
steady deposition 
which begins at that 

point of one or another filing which is toward the anode or positive termi- 
nal, producing a set of "lines of flow" resembling the lines as shown by 
iron filings in a magnetic field of force. Figure 140 is a reproduction of 



Fig. 140. A Current Sheet. 



EXPERIMENTS 



305 



the lines as they appeared after the paper was dried and the filings were 
brushed of. A T-shaped piece of lead was laid between the electrodes, and 
as this was a better conductor than the solution, the lines of flow, both 
from A to the point of the T and from the head of the T to B, are very 
significant. There is no magnetic action or magnetic substance in the 
experiment. 



Experiment No. 
Art. 216. 



88. — To Illustrate Polarization and Depolarization , 



A vessel 5 to 10 cm. in diameter (Fig. 141) (a common table tumbler 
will answer) contains a layer of mercury. On this is a layer of strong solu- 
tion of common salt (sodium 
chloride). A copper wire Cu 
is dipped into the mercury, the 
copper being insulated where 
it is in the salt solution, and 
a zinc plate Zn is supported 
in the solution, near but not 
touching the mercury. If the 
circuit is completed externally 
through an electric bell the cell 
will cause the bell to ring at 
first strongly, but rapidly di- 
minishing in intensity, as a film, probably sodium amalgam, forms on the 
mercury. This is cleared up promptly by putting into the liquid a very 
few grains of mercuric chloride (corrosive sublimate), which reacts to pro- 
duce sodium chloride and mercury; the depolarization is immediately ac- 
complished, and the bell again rings until the current is again checked by 
polarization. If the mercury surface is not bright and clean at first, a few 
granules of the mercuric chloride are needed to start the action. 




Polarizing and Depolarizing Cell. 



CHAPTER VI. 

LIGHT. 

226. Nature of Light. — (a) Periodicity. — In Art. 112 it was 
stated that " to prove that any phenomenon is due to wave 
motion it is sufficient to show, first, that it is periodic; second, 
that it is propagated with a finite velocity." Periodicity in 
light is most readily evidenced by phenomena of interference. 
Interference phenomena, which show regions of reinforcement 
and of destruction that do not shift, could only arise from periodic 
action in the agent, and such phenomena are easily seen to 
characterize light, in the succession of light and dark bands from 
two glass plates separated by a thin film of transparent substance 
reflecting (or transmitting) monochromatic light, or from the 
successive spectra when composite light is so reflected (or trans- 
mitted). Nothing is concerned in the phenomenon but light 
itself, and periodicity is at once established. 

Newton's rings, and other interference bands are examples. 

(b) Velocity. — That light is propagated with a finite velocity, 
i.e., that it requires time to proceed from one place to another, 
has been established by at least four methods, two of which are 
astronomical and two terrestrial. 

(1) In 1676 the Danish astronomer Roemer observed that 
eclipses of Jupiter's moons recurred at times earlier than the 
average, when the earth was at the position in its orbit nearest 
to Jupiter, as at A, Fig. 142; and later than the average when 
the earth was at the opposite side of its orbit from Jupiter, as at 
B. In the former case the eclipse is observed after light travels 
from m to A ; in the latter not until light has traveled from m to 
B, and the difference of time, or the time by which the eclipse is 
delayed, represents the time required for light to traverse the axis 
of the earth's orbit, or the distance AB. It amounts to almost 

306 



NATURE OF LIGHT 307' 

exactly 1000 seconds (998). As the axis of the orbit is about 
186,000,000 miles, this gives for the velocity of light about 186,000 
miles per second. This method, dealing with long distances, 
involved quantities that were thought to give the results a high 
degree of credibility and probability; but the distance of the 



-*T— — 



Fig. 142. Eclipse of Jupiter's Moon. 

earth from the sun is computed by the use of an angular quantity 
known as the solar parallax, which is the angle at the center of 
the sun formed by a line to the center of the earth and one tan- 
gent to the earth. This quantity is more accurately known now 
than it was in Roemer's day, but is still given with a considerable 
probable error as 8". 80. 

(2) About fifty years after the application of Roemer's method 
came another method due to the discovery of the aberration of 
light by the English astronomer Bradley. This is also an as- 
tronomical problem and depends upon the velocity with which 
the earth moves in its orbit, and this, in turn, is deduced from 
the size of the orbit or the distance from the earth to the sun, the 
calculation of which, as before, depends upon the sun's paral- 
lax. But as an independent astronomical method it may be 
presented in outline. In the first place let us deal with quantities 
for illustration, more readily within reach of our conceptions than 
the velocity of light. 

Imagine a perfectly calm day with rain falling, and, because 
of calmness, falling vertically. If we stand quietly and observe 
it, it will seem to us to fall from the zenith. But if we move on- 
ward at a given velocity the rain will seem to approach us or fall 
in a slanting direction. A tube, which at rest permitted rain to 



308 LIGHT 

fall through it while in a vertical position, must now be inclined 
with the top advanced toward the point approached if the rain 
is to go through without coming in contact with the sides of the 
z tube. The rain will seem to fall from a point dis- 

placed from the zenith in the direction in which 
the observer is moving. This changed direction is 
the resultant of compounding the downward ve- 
locity of the rain with a backward velocity equal 
to that with which the observer is advancing. A 
similar effect occurs if we travel to meet or cross 
the path of any other moving object. In Fig. 143, 
S1S if ZO represent the actual motion of the rain, and 
Fig. 143. Aber- QF that of the ODS erver, ZB will represent the 

ration. 

apparent motion 01 the ram. 

Now the earth is moving around the sun in nearly a circular 
orbit at about 20 miles per second. The light coming to us from 
a fixed star makes the star appear to us always somewhat out 
of its true position, displaced towards a point 90 in advance of 
the heliocentric position of the earth. As the earth completes 
its revolution about the sun the apparent position of the star 
describes a corresponding, but very small, ellipse against the 
dome of the sky, about its true position. The angular displace- 
ment, however, may be pretty accurately determined, and from 
that the ratio of the velocity of the earth to that of light itself. 
"The maximum angular displacement thus observed is only 
about 20^" ... or such an angle as would be subtended by a 
six-inch rule at the distance of one mile." (Stokes, Lectures on 
Light, First Series, p. 10.) The best results give for the ratio of 
these velocities, 0.0000994. But the final value of the velocity 
of light depends here upon the motion of the earth in its orbit; 
taking the mean distance of the sun to the earth as 93,000,000 
miles, the velocity of light, by eclipse of Jupiter's moons, is 
302,300,000 meters per second; by aberration of light, 299,300,000 
meters per second. 

(3) Fizeau's Method. — The methods of determining the veloc- 
ity by dealing with terrestrial magnitudes only, are those origi- 



NATURE OF LIGHT 



3°9 



nally employed by Fizeau in 1849 an d Foucault about "1854. 
Improved determinations upon these methods have been made 
in recent years. The method adopted by Fizeau was essentially 
as follows: 

Light from a slit s (Fig. 144) is reflected by a mirror m to a 
distant mirror M. In the path of this light is a toothed wheel W. 
If the wheel is slowly rotated, light passing between two teeth 
can go to M and return before it is obscured by the next tooth, 

w 



M 



'E 



Fig. 144. Velocity of Light by Fizeau's Method. 

and therefore the eye at E can perceive the light from S. If W 
is rotated at such a speed that any light from m passing between 
the teeth can go from W to M and back to W in just the time 
for the opaque teeth to move into the path of the returning light, 
i.e., to where the open spaces were, the returning light is inter- 
cepted and the eye cannot perceive it; by increasing the speed 
of W light again appears dimly and increases to a maximum when 
the returning light is perceived not through the same spaces 
through which it went out from W to M but through the next 
ones. Still higher speed of W again obscures the light. By care- 
ful determination of the speed of W and consequently of the time 
to turn through the space from one tooth to another, and by 
measuring the distance from m to M, the velocity of light was 
determined. With this distance equal to 8333 meters (a little 
over five miles), the wheel having 720 teeth, it was making 12.6 
revolutions per second at the first eclipsing of the light. This 
gives for V, 312,274,000 meters per second. 

(4) FoucaulVs Method. — In Fig. 145, s is a slit perpendicular 
to the plane of the paper, R a rotating plane mirror, L a lens of 



3io 



LIGHT 



considerable focal length. For a certain position of R, light 
coming from s will form an image of s on the plane mirror M, and 
the axis of the pencil of light will retrace itself, and the whole 
pencil will be reversed, M being placed at right angles to RL. 




Fig. 145. Velocity of Light by Foucault's Method. 

Now if " in the time occupied by the light in traveling from R 
to M and back, the revolving mirror has not appreciably altered 
its position, the return pencil will be reflected back to 5 and an 
image of the slit formed which will coincide with s. If, however, 
the mirror R be revolving rapidly in the direction indicated by 
the arrow, so that by the time the pencil reflected by M reaches 
it, it occupies the dotted position, the image of the slit formed by 
reflection will no longer coincide with 5 but will be displaced to 
some poiut s f to the left of s; and the amount of this displace- 
ment will depend on the rate of rotation of the mirror and the 
time occupied by the light in traveling from R to M and back." 
(Glazebrook, Physical Optics.) 

To determiue the velocity of light, measure ss\ sR, RM, and 
the rate of rotation of R. 



NATURE OF LIGHT 31 1 

Let ss f = 8, sR = a, RM = c, V = velocity of light. 

r = time for light to traverse 2 RM. = angle turned by R 
in time r, N = number of complete revolutions of R in one 
second. Then in one second the mirror turns through the angle 
2 wN, and in r seconds, 2 tNt. Thus, 6 = 2 ttNt. 

By turning the mirror through an angle 6 the reflected ray has 
been deviated from Rs to Rs f ; therefore, angle sRs f = 2 0; also 
ss' = sR.t&n sRs', or 8 = a. tan 2 6, so that 8 = a. tan 4 tNt. 
But r = the time for light to travel the distance 2 RM, 

2C , 8 tNc . 

.'. t=— . .'. 8 = a. tan Tr > 

V V 

but we may take 2 = tan 2 and consequently 

8 7riVc , TZ ZivNac 
8 = a. — r— , whence v = 

Professor Michelson employed values a = 8.58 meters, c = 605 
meters, iV = 257. The observed value of 8 was 0.113 meters, 
whence V = 296,500,000 m./sec. His final result, making all 
corrections, gave for velocity in vacuo, 299,940,000 meters per 
second. 

By Fizeau's method, repeated by Cornu in 1876, 

V = 300,400,000. 

Fizeau's method, by Forbes and Young, later, gave 

V = 301,382,000. 

The mean of reduced values gives as the best result a velocity 
of 300,574,000 meters per second for white light in a vacuum. 
This is 186,770 miles per second. 

As there is a small margin of error even in this mean result it 
is usual to take the even figure 300,000,000 meters per second 
as the velocity of light. This is 186,400 miles per second. (An 
account of the four methods is given briefly in Watson's Physics, 
Arts. 365-369, and in Hastings and Beach, Art. 543.) The 
velocity is different in different media. 

The periodicity of light and its velocity having been estab- 



312 LIGHT 

lished, those phenomena which characterize wave motion gen- 
erally, are readily recognized in connection with light. 

(c) Character of Vibration. — It will be seen, however, that 
certain phenomena can only be accounted for by supposing that 
the medium transmitting the waves is put in oscillation trans- 
versely to the direction in which the disturbance progresses; i.e., 
the vibrations of the ether are said to be transverse. 

It is difficult to understand how a fluid, as the universal ether 
is usually called, and especially a fluid so exceedingly rare as the 
ether is, can sustain a shearing stress, which is necessary in the 
ordinary view of elastic transverse vibrations. Even with small 
density the elasticity must be very high to give so great a velocity, 
which, as we have seen, depends upon the ratio of the elasticity 
to the density. So great is this stumblingblock that the ether 
has been boldly treated as an elastic solid in explaining light. 
(See especially Sir Wm. Thomson's (Lord Kelvin's) lecture on 
The Wave Theory of Light, in Popular Lectures and Addresses, 
Vol. I, Macmillan Company.) 

But Clerk Maxwell evolved a theory of the propagation of 
electromagnetic waves that provides for a disturbance of mag- 
netic character in one direction simultaneously with one of an 
electric character in a direction at right angles to this, and which 
includes light as one form of electromagnetic disturbance. This 
is known as the electromagnetic theory of light. 

227. Waves and Rays. — Light proceeding from a point 
through any medium will always progress a definite distance in 
a given time, and if the medium is homogeneous, this distance 
will be the same in all directions and the boundary of the region 
through which the disturbance has progressed will be the surface 
of a sphere. This surface will comprise the wave front from the 
source out in any direction. At a given point of the surface a 
normal line will be the direction of the progress of light at that 
point. A line traced from the source continuously perpendicular 
to the wave fronts is a ray of light. In a homogeneous medium, 
or in one throughout which light travels with the same velocity, 
the ray is straight, and in such a medium light travels in straight 



REFLECTION AND REFRACTION 



3*3 



lines, but only in such media. If the medium is one in which 
light travels at different rates in different directions, then the 
ray may be curved. If 
Fig. 146 represents a 
vertical plane section 
of a medium in which 
light from goes in 
the horizontal direction 
twice as fast as in the 
vertical, then the wave 
fronts would not be cir- 
cles, and horizontally 
and vertically the ray 




Fig. 146. Curved Rays of Light. 



would be straight, but along other paths it would be curved. 

228. Reflection and Refraction. — Light arriving at the sur- 
face of any medium is either absorbed by the medium, in which 
case its energy is usually changed into some other form, or it is 
transmitted through the medium, or it is reflected. It may be 

affected in all three 
of these ways. That 
part that is reflected 
conforms to the laws 
generally applicable 
to waves. 

For that which is 
transmitted, suppose 
mn (Fig. 147) to be a 
plane wave front pro- 
ceeding in air and 
arriving at a surface 
SS of water. If the 
velocity of light in 
water is less than that 
in air, say, three-fourths as great, by the time the wave front in 
air would progress the distance mo, or the disturbance at m would 
reach 0, that at n would advance into W a distance three-fourths 




Fig. 147. 



Change in Position of Wave Front by 
Refraction. 



314 LIGHT 

as great as mo, and would therefore be somewhere on a semi- 
circumference described about n with a radius nv equal to f mo. 
In the same way, while the disturbance is going from u to o that 
from t goes a distance f uo, and in the water the wave front will 
have the position ov, and the direction of the light will change 
from mo to ow. 

A change in the direction occurring when light passes through 
media in which its velocity is different is called refraction; the 
angle made by the wave front before refraction with the surface 
at which the refraction occurs is called the angle of incidence i, 
and that by the wave front after refraction is called the angle of 
refraction r. For two given media, no matter what may be the 
angle of incidence, if the light enters the second medium at all 

the refraction will be such that — — = /*, where /jl is constant for 

smr 

fflO 

the same two media. This is seen from the figure; for — = sin i, 

no 

,nv . ., - mo sini , , mo velocity in air 

and — = smr, therefore — = - — ; but — = — - — ; — -. , 

no nv sin r nv velocity in water 

sin i 
a constant ratio; so that — — is constant and equal to the ratio 

smr 

of the velocities in the two media. This ratio is called the index 
of refraction for the two media. 

When the direction of the light is considered by means of rays, 
the direction of the incident ray is perpendicular to the incident 
wave front, that of the refracted ray is perpendicular to the re- 
fracted wave front, and the angle of incidence is the angle be- 
tween the incident ray and a line perpendicular to the interface 
of the two media, while the angle of refraction is that between 
the refracted ray and the normal to the interface. Evidently 
the sines of these angles are in the same ratio as before. 

This " law of sines," sometimes called Snell's law and some- 
times the law of Descartes, was determined in the first place 
experimentally, and was part of the evidence to establish the 
wave theory of light when taken in connection with the fact, also 
determined experimentally (by Foucault), that light travels more 
slowly in the more highly refractive medium. 



REFLECTION AND REFRACTION 3 15 

In a medium of the same nature the refractive power increases 
with the density, and usually, of different substances, the denser 
is the more highly refractive, so that it is often stated that a ray 
of light in passing from a rarer into a denser medium is bent 
towards the normal; but this is not always true, and especially 
is it not true for gases. So the term " optically denser " has 
been employed to designate a medium which has a greater re- 
fractive power, whether its mass per unit volume is greater or 
less than that of the substance with which it is compared. 

If light is traversing a medium of the same nature but of 
changing density, it will undergo continual refraction and there- 




Fig. 148. Refraction of Light produces the Mirage. 

fore continual change of direction. This is familiarly seen in 
the effect of the atmosphere upon the sun's rays, by which the 
sun appears above the horizon when it is actually below it. (For 
curved path of light through a solution of varying density, see 
Wood, Physical Optics, p. 90.) 

In a homogeneous medium, however, light travels at the same 
rate in all directions, the wave front is spherical, and a ray drawn 
perpendicular to a wave front at any point is perpendicular to 
all the successive wave fronts, its prolongation being then a 
straight line. 

A limited portion of a spherical wave front at a great distance 
from the source of light or the center of curvature is so nearly 



316 LIGHT 

plane that the normals to it or the rays are so nearly parallel as 
to be called parallel light. Light from a source at an infinite 
distance is parallel light, and the light from the heavenly bodies 
is practically so at the earth. 

Change in the direction of light by diffraction will be considered 
later. 

229. Optics, Geometrical and Physical. — That branch of 
Physical Science that treats of Light is Optics. For the purposes 
of specialization it is sometimes divided into Geometrical Optics 
and Physical Optics, but we shall not follow such distinction 
further than to define it. Geometrical optics " treats of the 
propagation, reflection, and refraction of light according to defi- 
nite laws; and the utilization of such reflection or refraction in 
various optical instruments." Physical optics " deduces those 
laws as consequences of a certain hypothesis as to the nature 
of light, and in addition explains numerous phenomena which 
geometrical optics leaves unaccounted for." (Glazebrook, 
Physical Optics, Preface.) 

230. Light Invisible. — Light is the agent external to ourselves 
that gives us vision, but we must not forget that, although it is 
by means of light that objects become visible to us, light itself 
is not visible. If light were corporeal it ought to be visible, but 
when we fancy we see the rays it is not so. Light is not a thing, 
but a revealer of things. It is itself and by itself absolutely in- 
visible. View the heavens on a clear Winter night when the land 
is covered with gleaming snow and the dome of the sky is studded 
with glittering stars. Each star is a sun like our own, sending 
its light throughout space to all the other stars, and visible to us 
by the light it is sending to us, yet when we look sideways at the 
light thus passing from star to star, we cannot see it; space is 
black though flooded with light. Even the light of our own sun 
that is then streaming past the earth cannot be seen. 

231. The Seeing of Objects. — Objects that are not primarily 
luminous, i.e., that do not of themselves emit light, are seen by 
scattered reflection. A perfectly reflecting surface would reflect 
all the light that fell upon it according to the laws of reflection, 



IMAGES, REAL AND VIRTUAL 3 1 ? 

and light so reflected would reveal to the eye the source of the 
light before reflection, and the reflecting surface would not be 
visible. This is called specular reflection. With surfaces not 
well polished light is reflected in various directions, and in count- 
less variety of condition; every point of the surface becomes a 
luminous point from which light proceeds in all directions, and 
if by the eye or any other means we collect and converge these 
rays we form an image of these innumerable points that are 
secondary sources of light, and so form an image of the surface 
of the object. The difficulty of seeing a surface is in direct pro- 
portion to the perfection of its polish; hence the frequent blunders 
and deceptions arising from the use of fine mirrors in rooms or 
halls. (Examples.) 

No matter what may be the position of the source from which 
light has proceeded in the first place, when the light enters the 
eye we locate the source by the direction of the line by which the 
light entered the eye, so that the apparent position of the source 
may be very different from its real position; it may be exactly 
reversed, as when, by the use of two mirrors, one sees the back 
of his head in front of him. (Here the change of direction of 
light is due to reflection. Fig. 148 shows how, by means of re- 
fraction, one might perceive the inverted image of vegetation 
above a glaring surface, producing the mirage of trees upon the 
edge of water.) 

232. Images, Real and Virtual. — While the propagation of 
light is a wave phenomenon, the representation of it is sometimes 
simpler by means of rays than by wave forms. We shall have 
recourse to either as may seem better suited to our immediate 
purpose. 



3i8 



LIGHT 



By Waves. 

When a disturbance is progress- 
ing through a medium in the form 
of waves, the wave front may be 
either concave, convex, or plane. 
If the disturbance proceeds from a 
point, the wave front is necessarily 
convex. This form may be changed, 
however, by encountering a different 
medium so that it may become plane 
or even concave, and in the latter 
case its further progress will be to 
converge upon a point. Such a 
point is said to be the real image of 
the point from which the light pro- 
ceeded. 

If, upon the passage from one 
medium to the other, the wave front 
becomes less convex, the disturbance 
will seem to come from a point be- 
hind the starting point. If the wave 
front becomes more convex, the dis- 
turbance will seem to come from a 
point in front of the starting point. 
In either of these cases, this second 
point is said to be the virtual image 
of the point from which the disturb- 
ance actually proceeded. 



By Rays. 

When rays proceed from a point 
in all directions they are divergent, 
but upon encountering a different 
medium they may be rendered par- 
allel, or convergent upon another 
point. This point is said to be the 
real image of the point from which 
they proceeded. 



If, when the rays pass from one 
medium to another, they are ren- 
dered less divergent than at first, 
they appear to come from a point 
behind the actual starting point. 
If they are rendered more divergent 
they appear to come from a point 
in front of the starting point. In 
either of these cases, this second 
point is said to be the virtual image 
of the point from which the rays 
actually proceeded. 



These ideas may be illustrated by the following diagram 
(Fig. 149) to trace the progress of a disturbance proceeding from 
P towards A through several media : 

(a) In Spherical Waves. — The diagram shows the intersec- 
tion of the spherical waves by the plane of the paper. 

Suppose DAD to be the interface between two media X and 
Y. When the disturbance reaches A, the wave front is CAC. 
If, now, Y is such a medium that a disturbance will progress in 
it a distance AB while it will go a distance CD in X, then the 
unmodified wave front that would have passed through DD in 
a curve, with P as a center, is now modified so as to pass through 



PATH OF LIGHT THROUGH SEVERAL MEDIA 



3 J 9 



DBD, which may be a straight line, and the wave front will have 
become plane, and will move on as such if the medium Y is 
homogeneous. Whether this will be a plane front is found to 
depend on the nature of the two media, the curvature of the 
incident wave front and that of the interface DA D. 




Fig." 149. 

If the next boundary of Y be EGE, the wave front EFE will 
undergo a change of curvature, and if the third medium Z is such 
that a disturbance may progress from E a distance EH in the 
time that a disturbance goes from F to G, the wave front will pass 
through HGH, and thereafter advance in waves converging upon 
P r which is the image of P. 

The interface between Y and Z might have a form like EKE, 
such that a disturbance from a point L on the wave front LKL 
could go as far as LE in the medium Y while one would go in 
the medium Z from K the greater distance KN. Then the wave 
emerging beyond E would have the form ENE, and would pro- 
ceed in expanding spheres as if proceeding from a center at P". 
P" is then the virtual image of P. 

At either surface also the form of wave front may be so modi- 
fied by reflection as to cause an image by the waves being re- 
versed and made to return in the same medium through which 
they advanced. This image will be real if the reflected waves 



320 LIGHT 

really converge upon it, and virtual if they appear to proceed 
from it. The virtual image will be behind the reflecting surface, 
if this surface is plane or convex. 

(b) The corresponding constructions with rays would be as 
follows: A ray from P normal to the interface at A or G con- 
tinues without deviation. An oblique ray, as PD, will be de- 
flected as along DE, the change of direction depending upon the 
obliquity of the ray and the nature of the two media. At E, on 
again changing the medium of propagation, the course is again 
altered and the refracted rays intersect at P', which is the image 
of P. The second interface might have a form EKE such that 
the emergent rays would diverge instead of converging, and then 
they would appear to proceed from a point P" which is the virtual 
image of P. 

Either mode of construction is justifiable (by waves or by rays), 
and if they are both made for the same media, the same forms 
of surface and the same position of P, they would give the same 
resulting images when applied to reflection as well as to refraction. 
The positions of a point of light and its image are said to be 
conjugate to each other; i.e., if the former is put in the position 
of the latter, the latter will occupy the position of the former. 

233. Critical Angle ; Total Reflection. — As light emerging 
from an optically denser to an optically rarer medium is refracted 
from the direction normal to the surface between the two media, 
making the angle of refraction greater than the angle of incidence, 
it follows that while the angle of incidence is still less than a 
right angle the angle of refraction may equal 90 and the re- 
fracted ray lie in the surface between the two media. If the 
angle of incidence be now further increased, to pass into the 
second medium, the law of refraction would result in the emergent 
ray making an angle with the normal greater than 90 , so that 
emergence is impossible. 

Suppose, in Fig. 150, NQ is such a surface of separation, and 
light from P makes an angle of incidence NPQ such that the 
refracted ray QR lies in the surface NQR ; the angle NPQ then is 
called the critical angle for those two media. Light from P in a 



CRITICAL ANGLE; TOTAL REFLECTION 



321 



direction at an angle with PN greater than the critical angle will 
not pass into the second medium, but will be totally reflected into 
the first medium, giving the most perfect reflection possible. 




Fig. 150. Total Reflection. 

The angle of incidence at this critical stage is obviously deter- 
mined by the condition 

x , , c sin i sin critical angle 

Index of refraction = - — = ; — - — 

sin r sin 90 

Calling the index of refraction /*, 

Critical angle = sin -1 /*. 

For light passing from water to air, 

M =- =0.75 = sin48°35'. 

4 

From crown glass to air, 

M = - = 0.667 = sin4i°48'. 
3 

From bisulphide of carbon to air, 

1 



1.63 



0.6135 = sin 37 51'. 



If an eye at P looking up could see in the first medium by direct 
view only objects within the cone QPQ', it could see in the second 
medium objects within the whole range of the horizon. It would 
have no difficulty in seeing round the corner at Q. (See the 
" fish-eye " views by Professor R. W. Wood, Wood's Physical 



322 LIGHT 

Optics, p. 67.) An object at S would appear brilliantly by total 
reflection at T to be at S f . 

Experiment No. 8g, page 349. — Total Reflection by Luminous Jet. 

234. Apparent Depth of a Transparent Medium. — It may be 

shown (see Hastings and Beach, General Physics, Arts. 546, 547) 
that, in general, when the wave form is modified by reflection or 
refraction at a surface, if 

7 = curvature of surface at which wave is modified, 

(curvature = 



\ radius, 

C = curvature of the incident wave front, 

Ci = curvature of the modified wave front, and p = ratio of 

velocity of light after modification to velocity before 

modification, 

then C\ = pC + (1 — p)y. (An important formula.) 

Let P (Fig. 151a) be a point in a transparent medium, as 
water, to be viewed by the eye vertically above it in a dif- 
ferent medium, as air. If the velocity of light in the medium 
above N were the same as below, the wave fronts would be 
spherical surfaces about P as a center, and the eye would see 
P in its true position. But if the velocity in air is, say, four- 
thirds that in water, then the emergent wave instead of hav- 
ing the unmodified form o'no' will have the greater curvature 
of o'n'o' ', for while the disturbance goes from to 0' ', that 
from N will go to n f where Nn r is p times Nn, and the center 
of the new wave system will be at P r , and to the eye the light 
will seem to come from P' ', or P will appear to be at P' . If 
P is at the bottom of the lower medium the apparent depth will 
be NP' instead of NP. In the case of a plane surface, 7 in the 
above equation is zero and d = pC; for water and air p = |, 
or the curvature of the wave entering the upper medium at N is 
four- thirds that of 0N0 or the radius P r N is f P N, or the appar- 
ent depth is i/fj, times the real depth, p. being the index of refrac- 
tion from the second medium into the first. 



APPARENT DEPTH OF A TRANSPARENT MEDIUM 



3 2 3 



The corresponding construction by rays would be as follows: 

If ME (Fig. 15 ib) is the limiting ray from P that can enter 

the eye after refraction at the surface M N, to the eye the light 

will appear to come from P', and the apparent depth will be 

















































(E 



T7 

// 

77 

rt 

pi 'j : 

ji ~ 

" P 



(a) (b) 

Fig. 151. Thickness of a Transparent Layer apparently reduced by Refraction. 

NP' instead of NP. The angle MPN is the angle of incidence 
i, and MP' ' N the angle of refraction r. In the triangle MPP', 

MP sin MP'P 



MP' sin MPP'' 

4l _ , MP sinr 
therefore 



But sin MP'P = sin MP'N = sin r, 
= ix, if fx is the index of refraction from 



MP' sin i 
the upper medium into the lower. 
The pencil of light entering the eye is very narrow, both i and 

It 



MP . NP 

r are small, and the ratio of 7-— 7 is very nearly that of — — -. 

MP' J J NP' 



becomes more and more nearly equal to it for light that is more 
and more nearly along the normal line P N. Thus, for perpen- 

ju. In the case of water and air, /* is f , 

and the apparent depth is three-fourths the actual depth. 



NP 

dicular viewing,—, 



324 LIGHT 

Examples. — 

i. If the index of refraction for light passing from air into water is I, 
and the velocity of light in air is 299,000,000 meters per second, what is its 
velocity in water? Am. 224,250,000 m./sec. 

2. If a right-angled glass prism have all three faces polished, trace a ray 
of light that falls perpendicularly upon one of the faces forming the right 
angle, the index of refraction of the glass being 1.5. 

3. A plate of clear glass 1 cm. thick, whose refractive index for light from 
air into the glass is 1.5625, is laid upon a line of printing. How far below 
the upper surface of the glass will the letters appear to an eye looking ver- 
tically down upon them? (NP' } Fig. 151.) Ans. 6.4 mm. 

235. Foci. — When light diverging from any point is so 
changed in direction by reflection or refraction as to pass really 
or apparently through another point, the second point is the 
image of the first. The positions of the source and the image 
are interchangeable. The point to which the light converges or 
from which it appears to diverge is called a focus. 

The usual means of producing images are mirrors and lenses, 
and commonly these have plane or spherical surfaces. A plane 
surface may be treated as that of a sphere whose radius is infinite 
or whose curvature is zero. A line passing through the center of 
the sphere and perpendicular to the plane cutting the lens or 
mirror surface from the sphere of which it is part is the principal 
axis. Light from a point on this axis has its focus also on this 
axis, and when the light is parallel or proceeds from an infinite dis- 
tance, and is parallel to the principal axis, the focus is called the 
principal focus of the mirror or lens. Light from a luminous 
point at the principal focus would become parallel light after 
modification by the apparatus (lens or mirror). Light from an 
object at a finite distance comes to a focus, that is, it forms an 
image, at a position such that if the object were placed there its 
image would then be where the object had been. These are said 
to be " conjugate positions," or a luminous point and its image 
are conjugate foci. For spherical mirrors of small angular aper- 

ture and radius R, the principal focal length / is — , and the 

2 

relation of conjugate foci is 7 + 7 = 7; = 7- 

7i h K J 



FOCI 



325 



Demonstration, (a) By Rays. — In Fig. 152 (a), let PP n 
represent a concave section of a spherical mirror with center 
at C and radius of curvature CA = R. Let F be the middle 
point of CA. Light rays parallel to the axis FA striking the 
mirror at any point as P' are reflected, making the angle of 
reflection CP'F' equal to the angle of incidence CP'L. Since 
LP' and CA are parallel Z LP'C = Z P'CA. :. Z P'CF' = 
Z CP'F, and P'F' = CF'. As the portion of the arc AP 
by which the rays are reflected is taken smaller and smaller, 
P'F' becomes more nearly identical with AF', and F' becomes 
more nearly identical with F, so that for a small angular aper- 
ture AP', the principal focus is practically midway between 




L 


"^-Vi 


"v- v 




p7 


'^ X v 




a! 


p c 



(b) 



Fig. 152. 



C and A, or at F. Rays which proceed from F as an origin 
are reflected parallel to the axis CA . 

If the rays L fell upon the convex side of the mirror as in 
Fig. 152 (b), at the points P, they would, after reflection, not 
pass through F at all, but would diverge as if they had come 
from F behind the reflecting surface. The point F is then a 

r> 

virtual focus, and the focal length of the mirror is — as before. 

2 

For conjugate foci, suppose rays to proceed from F\, Fig. 
152 (a). Such a ray is reflected at P to F 2 , the angles of inci- 
dence and reflection F\PC and CPF 2 being equal, say = i. 
Call the distance F X A =f h F 2 A = f 2} Z PF X A = 5, Z PC A = 6, 
and Z PF 2 A = 4>. Then 

4> = + i, 

6 = 8+i; 



326 LIGHT 

cf> - 6 = d - 8; 
or 

8 + 4> = 26. ...... (1) 

AP AP AP 

If arc AP is small, S = — -, = — -, and 6 = — -, and these 

71 h *■ 

,,.,,,. , , . ^P . AP 2AP i,i 2 

substituted in (1) give —- + —- = -—- or - -f - = -; 

yi 72 a ji f 2 R 

and if /1 = 00 the incident rays are parallel, f 2 = principal 

1 2 
focal distance/, and - = — . Q. £. /). 

(6) 5}» waves. — By applying the general formula at the be- 
ginning of Art. 234, waves proceeding from a point at a dis- 
tance /1 have a curvature at the mirror such that C = — ; on 

h 
reflection they meet really or apparently in a point at a distance 

/2, so that C\ = — ; also *v = — and p = — 1, and the formula, 

72 R- 

becomes 

I I . 2 1,12 / N 

/i = -/7 + p or h+rri- ■ • • (2) 

If the incident light is parallel light, the distance / of the prin- 
cipal focus is called the focal length of the mirror or lens. In 
such case the incident wave front is plane, C = 0, f 2 becomes /, 

and we have - = ", so that for conjugate foci, — + — = — = -. 
/ R Jl J2 R f 

Q. E. D. 

If the distance / measured in front of the mirror is positive, 
either f\ or f 2 in the equation might be negative, which would 
mean that it was measured back of the mirror. 

For lenses the principal focal distance is given by the equation 

^=(m-i)^-A (3) 

/ Vi r 2 J 

where \x is the index of refraction from air into the glass of which 
which the lens is made (also the ratio of the velocity of light 
in air to that in the glass) and r\ and r 2 are the radii of cur- 



FOCI 327 

vature of the lens surfaces, with opposite signs if the faces 
of the lens are curved in opposite directions. (For demonstra- 
tion of this see Watson's Physics, Arts. 340, 351, and 352.) 
The conjugate focal distances, however, may be expressed in 

terms of the principal focal length by the relation - = 1 — 

/ / 1 h 
where / is + for a converging and — for a diverging lens. (See 

p. 330, and for demonstration see Mumper's Physics, Art. 206.) 
As an illustration, suppose in Fig. 153, LL is a lens of negligi- 
ble thickness whose one face is plane and the other is spherical 




Fig. 153- 

with a radius of curvature of 5 cms. Light proceeds from a 
point P on the axis at a distance of 30 cms. from the lens. The 

velocity of light in air is - the velocity in the glass. From the 

2 

formula of Art. 234, C\ = pC + (1 — p)y. Here, for the light 

2 1 

passing from P into the lens, p = -, C = — , and 7 = 0. These 

3 30 

21/ 2\ I 

in the formula give Ci = - X — + ( 1 )o = — . If the 

3^ 3° V 3/ 45 
thickness of the lens is negligible, we may suppose the waves 
immediately to emerge from the lens into the air through the 
curved surface of the glass. In the general formula this value 
of C\ now takes the place of C. The wave has the curvature 

— , p = -, and y = -. Then the emergent wave will have 
45 2 5 

curvature C'\ = - X h (1 — -)- = • The direction 

2 45 V 2/5 I 5 > 

of curvature is reversed and the diverging light from P con- 



328 



LIGHT 



verges upon P' on the other side of the lens, at a distance of 
15 cms. from it. 
Or thus: From Eq. (3) we may find for the lens LL: 



OO C/ 10 



Then for the conjugate focal distances /1 and/2 we have/i = 30 
and 



whence 



1 1 . 1 1 1 1 
- = T + T or — = h -, 



h J 5' 
or P' is 15 cms. to right of LL. 

In applied optics, if / is measured in meters, the quantity - 

measures the " power " of the lens or mirror in diopters, one 
diopter being the power of a lens whose focal length is one meter. 

236. Refraction of Light through a Plate with Parallel Sides. 
— If light pass from, say, air to glass in the direction RI (Fig. 
154), it is refracted in the direction 

IE such that ^— = /x. At E it 

sm (3 

emerges in a direction ER! such that 
sinff' _ 1 
sin a /x 

jS' = |8; then a = a, and ER f is par- 
allel to RI, a result verified by ex- 
periment. 

237. Images of Objects as Formed 
by Lenses. — The surfaces of a lens 
at points on the principal axis, as at M and N (Fig. 155), 
are parallel; also for a point P on one surface there is usually a 
corresponding point Q on the other surface such that the tangent 
planes at P and Q are parallel. A line joining the points P and 
Q cuts the principal axis in a point O called the optical center 



If GN is parallel to A M, 




Fig. 154. Passage of a Ray 
through a Plate with Parallel 
Sides. 



IMAGES AS FORMED BY LENSES 



329 




of the lens. Any incident ray RP, falling upon the surface PN 
in such a direction that by refraction it takes the path PQ, will 
emerge at Q in the direction QR r parallel to RP, and if the 
thickness of the lens is negligible, a point 
on RP will have its image on QR' '. All 
rays passing through are undeviated in 
direction. With a thin lens and points at 
a considerable distance, a line drawn 
through gives, with sufficient accuracy, 
the direction of the undeviated ray. With 
a double convex lens of like curvature on 
both sides, is at the middle of the glass. 
A line through other than the principal axis is called a sec- 
ondary axis, and the image of any point that is not on the prin- 
cipal axis is found on the sec- 
ondary axis through the point. 
Thus an image may be con- 
structed if the values of p and / 
are , known. In Fig. 156, the 
image of A is on the line AO\ 



Fig. 155. Optical Cen- 
ter of a Lens. 




Fig. 



156. Formation of an Image 
by a Convex Lens. 



that of B on BO at B' where ~ 

BO 



The intake of C is 



OB' f 

on CO. These relations, however, are only applicable to thin 
lenses with small angular aperture. With large angular open- 
ing from m to n, the rays from any point, as A , will not all 
intersect in the same point after reflection or refraction, and a 
sharp image will not be produced. This failure to come to a 
common focus on account of the sphericity of the lens surfaces 
is called spherical aberration. In photography, as in optical 
work with lenses generally, sharpness of image is gained by 
using a diaphragm so as to permit light to pass only through 
the central part of the lens; but this sharpness of definition is 
gained at the expense of the quantity of light, and consequently 
of brightness. 

The object and its image are at conjugate focal distances from 



330 LIGHT 

the lens, like the point of light and its image in Art. 232, and 
their sizes are as these focal distances. 

A converging lens (convex) is thickest at the middle and causes 
light which passes through it to be more convergent (or less 
divergent) than before; a divergent lens (concave) is thinnest at 
the middle, and causes light which passes through it to be more 
divergent (or less convergent) than before. Since these two 
types of lenses change the direction of the light in opposite ways, 
the former are sometimes called positive and the latter negative 
lenses. 

It is shown in higher optics that if two thin lenses are placed 
together the " power " of the combination, i.e., the reciprocal of 
the focal length, equals the algebraic sum of the powers of the 
two lenses separately. If /1 and/ 2 are the focal lengths of the two 
lenses, and F' that of the combination, 

F' h V 

if /1 or f 2 is for a divergent lens the sign of its reciprocal in this 
equation is minus. 

Examples. — 

1. If the focal length of a camera lens is 10 cm., how far behind the lens 
will be the ground glass to show a sharp image of an object that is one meter 
distant in front of the lens? How far if the object is 1 5 meters away? If it 
is 100 meters? Ans. 11.11 cm.; 10.06 cm.; 10.01 cm. 

2. In the second case, what would be the size of the picture of a house 
front 20 ft. X 30 ft.? Ans. 1.6 in. X 2.4 in. 

3. The distance of an object from a convergent lens is twice the focal 
length of the lens; show that the image and object are of the same size. 

At the front of the eyeball is a crystalline lens which, together with the 
humors of the eye, forms images on the retina, a membrane at the back of 
the eyeball (see Fig. 157). 

The distance from the lens to the retina is about 2.3 cm. The normal 
eye gives a distinct image of ordinary print which is at a distance of 25 cm. 
in front of the lens, but the latter, along with the rest of the eye, can so 
adapt itself as to make on the retina the image of objects that are at a 
greater or smaller distance than this. This change of the eye is called 
accommodation. If, however, the lens becomes too flat its focal length is 



IMAGES AS FORMED BY LENSES 



33 1 



increased (or,what is the same thing, its power is diminished) and the 
position of the image would be behind the retina except for distant objects. 
Such an eye is said to be far-sighted. If the lens is too much curved, the 
image is in front of the retina except for objects near the eye. Such an eye 
is near-sighted. These positions are illustrated in Fig. 157. If the image 
of an object at P is distinct on the retina at p, the eye is normal; but if the 
image is indistinct when the object is at P and is distinct only when the 
object is brought nearer, as at P' , the eye is near-sighted. In that case a 
sharp image of P is formed in front of the retina, as at p' '. If the image of 
an object at P is indistinct, but becomes distinct from a greater distance as 



Retina 



Vitreous Humor 

Crystalline Lens 




Fig. 157. Defects of Vision. 

P", the eye is far-sighted. In such case the position of a sharp image of P 
is beyond the retina, as at p" . 

In case of either of these defects, an auxiliary lens (spectacle lens) may 
be so combined with the lens of the eye as to make the focal length of the 
combination such that the image of an object 25 cm. from the eye will be 
formed, say, 2.3 cm. behind the lens or on the retina. That is, the power 

— - of the eye normally or of the combination should be 
F 

As illustrations, suppose (1) the eye sees print most distinctly at a dis- 
tance of 10 cm. It is near-sighted. The power of the eye is 



10 



o.535. 



fi 2.3 
It must be combined with a concave lens that will reduce the power to 

0.475; i- e -> a negative lens of power — = 0.06, or one whose focal length is 

h 
16.66 cm. 

(2) Suppose the eye sees distinctly not nearer than 40 cm.; it is far- 
sighted. The power of the eye is 

/l 2.3 4O 



O.46. 



332 LIGHT 

It must be combined with a positive (convex) lens to bring the power up 
to 0.475, or have a power 0.015, or a focal length f> = 67 cm. 

The power in these examples must be multiplied by 100 to give the 
power in diopters; in (1) the power of the auxiliary lens is 6 diopters, in 
(2) it is 1.5 diopters. 

Suppose the distance from the crystalline lens to the retina to have any 
fixed value, say C, in place of 2.5 cms. above, let d be the distance of dis- 
tinct vision for the eye tested, whether normal or abnormal, and 8 the 
proper distance for distinct vision, like the 25 cms. above, then the power 
of the eye is 

111 

iri + c ■ ■ (o) 

d may or may not be equal to 6, but it should be so, and a lens of power 

— must be combined with the eye so that the combined power shall be 
h 

1 1 1 1 

7Mn + c {h) 

The difference between the desired power represented by (b) and the 
actual, represented by (a), is the power of the auxiliary lens to be used. 

Subtracting (a) from (b) we have — = — — — . Obviously — is + or — 

J 2 5 d J 2 

according as d is greater or less than 5. 5 is usually taken as 25 cms. 

Of course, in practical optometry, many other things have to be taken 
into account besides the elementary features here considered. 

Examples. — 

1. A person holds his book within 9 cm. of his eye to read easily. What 
spectacle lens does he require? 

Ans. A concave lens of 14 cm. focal length. 

2. If he sees most distinctly at a distance of 80 cm. what lens should he 
use? Ans. A convex lens of 36.5 cm. focal length. 

Experiment No. go, page 350. — Show mirrors, lenses, production of 
images, foci, reflection, refraction, total reflection, etc., preferably by means 
of the optical disk if such is available. 

238. Photometry. — The term means measurement of light, 
but is commonly applied to any comparison of the illuminating 
powers of any different sources of light. This is generally accom- 
plished by comparing the illumination that is afforded by the 



PHOTOMETRY 333 

lights. By the illumination of a surface is to be understood the 
ratio of the quantity of light which it receives to the area over 
which the light is distributed, or the amount of light per unit 
area. By the illuminating power or the intensity of a light is 
meant the illumination it can produce at a unit's distance. This 
depends on the light itself, but the illumination of a surface varies 
directly with the intensity of the light and inversely with the 
square of the distance, so that if we call the illumination /, power 

of the light /, and distance d, we have / = ~ 

d 

All radiation proceeding from a point in straight lines will cover 
an area proportional to the square of the distance from the point, 
and therefore the quantity per unit area will be inversely pro- 
portional to the square of the distance. 

Different lights may be compared in intensity without express- 
ing either one in definite units, but to express the power of either 
one independently, a standard unit is necessary. For want of a 
satisfactory standard the measurement of illuminating power is 
among the least precise of physical determinations. The com- 
monest standard in English and American practice is the British 
standard candle, a spermaceti candle weighing six to the pound 
and burning 120 grains per hour. The French standard is the 
" Carcel," burning 42 grm. of colza oil per hour (equal to about 
g\ candles). In Germany the Reichs-Anstalt standard is a lamp 
burning amylacetate, the flame being adjusted to standard 
specified conditions. 

England, France and the United States of America have now 
adopted a common " International Candle " which is very nearly 
equal to the above British standard candle and equals -9 - Ger- 
man standard, and 0.104 Carcel units. 

If / is the power of the light, d its distance from a surface, and 

/ the illumination produced upon the surface, in general I — — ; 

and for the illumination resulting from two different sources, h, 
h, we should have 



h j t h 

d\ 



/, = -£;, and /, = -£- 



2' 



334 LIGHT 

and if the two can be so placed with reference to a given surface 
as to produce equal illumination of it, then h = I 2 , 

, h h h d\ 2 

and T2 = 7~2 or T = T~2> 

that is, the intensities of the lights are to each other as the 
squares of their distances from the spot which they illuminate 
equally. 

Experiments Nos. gi and g2, page 351. — Illustrate with Bunsen and 
Rumford photometers, and call attention to other forms and to special 
features in comparison of lights, as difference in color, etc. 

The comparison of the intensity (candle power) of two lights is 
usually effected by deciding when the two lights produce equal 
illumination of a given surface, i.e., make it appear equally 
bright, but the relative illumination of two surfaces that are not 
equally bright is determined by the amount of light per unit area 
on each surface. The common unit of illumination is the lux 
(plural lux), which means the illumination produced by a light 
of one candle power at the distance of one meter. 

Examples. — 

1. The shadow of a rod is cast upon a screen by a standard candle and 
by an incandescent lamp. When the shadows are equally lighted, the 
distance from the candle to the shadow cast by the lamp is 50 cm., and the 
distance from the lamp to the other shadow is 190 cm. What is the in- 
tensity of the lamp? Ans. 14.44 c.p. 

2. A candle is placed 30 cm. from one side of a cardboard screen, and 
a 10 c.p. gas flame is on the other side at a distance of one meter. Compare 
the illumination on the two sides. 

Ans. The side toward the gas flame is nine- tenths as bright as that 
toward the candle. 

3. A grease spot in a screen is equally illuminated by a candle on one 
side of it and a Welsbach incandescent mantle on the other side. The dis- 
tances of the candle and the Welsbach from the screen are 26 cm. and 200 cm. 
respectively. Compare the intensity of the two lights. 

Ans. Welsbach: candle = 59.17 : 1. 

4. Of three equal candles, two are placed together on one side and 
the third on the other side of a screen containing a translucent grease 
spot. The distance of the single candle from the other two is 150 cm. 



THE SPECTRUM: DISPERSION 



335 



How is the screen situated when the spot is equally illuminated from both 
sides? Ans. 62.13 cm. from the single candle. 

5. A lamp of 11 c.p. is placed 3 meters from a standard candle: deter- 
mine two positions in which a cardboard screen would be equally illuminated 
by the lamp and the candle. 

Ans. On that side of the candle toward the lamp, at a distance of 69.5 
cm. from the candle; and on the side away from the lamp at 129.5 cm. from 
the candle. 

239. The Spectrum ; Dispersion. — Although all colors falling 
upon a reflecting surface at a given angle are reflected at this 




A Red 

D Orange-yellow 



ff. Violet 



Fig. 158. Spectrum formed by a Prism. 

same angle, they are not equally refracted by the same refracting 
medium. When a narrow beam of white light falls upon the 
surface of a refracting medium, it is separated into a band of 
greater width, the most highly refracted part being violet in color 
and the least refracted red, with intermediate colors indigo, blue, 
green, yellow, orange, no one color sharply defined in limits but 
each merging into the next. This band of colors is called a spec- 
trum. It exhibits at once the facts that the light producing it is 
not simple but complex, and that its constituent colors are un- 
equally refracted, this unequal refraction constituting dispersion. 
If the light passes from air through a triangular prism, as in 
Fig. 158, further refraction occurs at the second face, causing a 



33& LIGHT 

further deviation of the light, and the spectrum is easily observed. 
A very narrowly limited portion, i.e., an elementary portion of 
any one color, if passed through another prism, will be again 
refracted, but not further separated. Of prisms of different sub- 
stances, as glass, water, etc., each has its own refractive power 
for the several colors of white light. The refractive power is 
determined by the least angular deviation which a prism of a 
given angle can produce in a given color. This is obviously 
greater for violet than for red. One substance, however, may 
refract the whole spectrum highly, but the violet not much more 
than the red; there would then be large deviation and small dis- 
persion, while another substance might have lower refractive 
power for every part of the spectrum, but relatively greater for 
the violet than for the red ; there would then be small deviation 
with large dispersion. The dispersive power of any substance as 
compared with that of another is the ratio of the difference in the 
angular deviation of two colors (i.e., the dispersion of those two 
colors) to the angular deviation of the mean ray between them; 
for example, the angle between AM and HM divided by the 
angle LMD. It is connected with the index of refraction by 

£ _ j 

the equation — - = — — — (see Watson, Art. 372), in 

dj) \±d — 1 

which 8 is the angular deviation and ix is the index of refraction. 
The first member of the equation is the dispersive power of the 
prism for the extremes of the spectrum. 

When the source of light is a narrow slit illuminated by an 
incandescent solid or liquid, the spectrum is a continuous band 
of colors, but when the light is that of a gas, the spectrum con- 
sists of one or more streaks of color with dark spaces between 
them. Moreover each gas produces a spectrum peculiar to itself, 
and distinguished from the spectrum of other gases by the colors 
of the lines and their situation. 

Experiments Nos. 93 and 94, page 351. — Continuous and Discontinuous 
Spectra. 

240. Chromatic Aberration. — Since the faces of a lens at any 
distance from the axis are inclined to each other, they correspond 



ACHROMATIC LENS 



337 



to the faces of a prism, and light passing through the lens is 
decomposed into colors, the violet being bent most toward the 
thick part of the lens. As a consequence the violet rays are 
brought to a focus nearer the lens than are the red rays, and the 
image is a colored one and not sharp. Such " going wrong " on 
account of color is called " chromatic aberration." 

241. Direct Vision Spectroscope. — By arranging two prisms 
of properly related refractive and dispersive powers, light may 
be dispersed and yet proceed from the last face in a direction 
which, for some portion of the spectrum, is parallel to that in 
which it came to the first face. There will then be dispersion 
without deviation (see Fig. 159). 




Violet 



Fig. 159. Deviation corrected while Dispersion is retained. 

242. Achromatic Lens. — If the angles and the material of the 
two prisms of Art. 241 are so chosen that the dispersion of two 
colors caused by one is neutralized by the other while the refrac- 
tion is not neutralized, there will be refraction, but the two 




Fig. 160. Dispersion corrected while Deviation is retained. 

colored images of the source of light will be brought to the same 
focus, and chromatic aberration for those two colors will be 
corrected, as in Fig. 160. The same principles apply to light 
passing through a corresponding combination of lenses, and the 



33§ 



LIGHT 



same results are obtained. A third lens or prism makes it 
possible to correct for three colors, and if these are blue, yellow 
and red, the correction is pretty complete for the entire spec- 
trum. Such a lens is called achromatic. It consists usually 
of a converging (double convex) lens of crown glass, for which 
the indices of refraction for the extremes of the spectrum are 
ix A = 1.528, fj, H = 1.55, and a diverging (double concave) lens of 
flint glass of which the indices of refraction are fx A = 1.578, and 
n H = 1. 614. 

243. Interference of Light. — Regarding light as a wave 
phenomenon, if two separate beams of light or two parts of one 
beam, proceeding from a common source and accordingly in the 
same phase of vibration, are so modified in their subsequent 
progress as to arrive at a point in opposite phases, they interfere, 
and a diminution or extinction of light occurs. Any color is 
" light," and it will be found that light of one color differs from 
that of another color only in wave length. The retardation of 
one part of a beam of light as compared with another part is 
accomplished in various ways, of which that by reflection from 
the two surfaces of a thin medium is one of the simplest. 

If the convex surface of a plano-convex lens with large radius 
of curvature, as C (Fig. 161), be placed upon a plane glass P, the 
surfaces will be in contact at 
the point of tangency 0, and 
will separate very gradually, 
with a thin layer of air be- 
tween them, whose thickness 
is calculable for any given 
distance from 0. A ray of 
monochromatic light I A en- 
ters C in the direction AB, 
at B is in part reflected to E and emerges in the direction ER. 
The other portion passes from B to C through air, is reflected to D 
and continues along DFR. If the air layer is very thin FR and 
ER enter the eye together, and if the path BCD is one half wave 
length of the light the second part of the light will, on this 




Fig. 161. Formation of Newton's Rings. 



INTERFERENCE OF LIGHT 339 

account, be a half wave length behind the first part, and theoreti- 
cally the portions ER and FR will interfere, and the eye will 
perceive a narrow dark circular band of which is the center and 
OC the radius. This will occur again at such a radius that the 
distance BCD is three, or five, or any odd number of half wave 
lengths ; where the distance is any multiple of whole wave lengths 
there will be a ring of light. This gives the series of so-called 
Newton's Rings. If the incident light is red, the rings will be 
only red and dark; if the color is yellow, the rings will be alter- 
nately yellow and dark, but the yellow rings will not occur at the 
same radial distance as the red rings, thus indicating that the 
different colors have different wave lengths. If the incident 
light is white there is a succession of circular spectra. 

Such, in brief, is the theory of the colors of thin plates. 

At the difference in the length of the paths is zero; here the 
waves would theoretically have no difference in phase, and the 
center would be bright; but wherever waves are about to proceed 
from a denser to a rarer medium reflection occurs with no change 
of phase, whereas, if reflection takes place at a surface where the 
wave is about to enter from a rarer into a denser medium, as at 
C, a reversal of phase occurs, and the reflected wave falls a half 
period behind in consequence of such reversal, and so the center 
is dark (see Art. 118). In the same way, where the distance 
BCD is a half wave length the total retardation is a whole period, 
and a bright ring is produced ; where the distance. BCD is a wave 
length the retardation is one and a half periods, and the ring is 
dark, and so on, the reversal of phase modifying the simple theory 
as at first presented. If the rings are viewed by the light trans- 
mitted through P the colors occur in the order first described, 
but they are not as brilliant as those produced by reflection. 

The beautiful colors of soap films, or of a very thin layer of oil 
on water, are due to interference, but here the thin plate is a 
liquid, instead of air as above. 

Note. — The illustration and explanation would be more rigidly correct 
if the incident light falls upon a plate of uniform thickness, as, e.g., the 
plate P instead of C, but the presentation here shown is a common one. 
Experiments Nos. 95, 96, 97, page 353. — Colors of thin plates. 



34Q 



LIGHT 



244. Diffraction; Measurement of Wave Length. — Light 
passing the edge of an opaque object is deviated both to one side 
and the other of the edge, from a straight direction, at an angle 
depending upon the wave length. Such deviation is called 
diffraction. 

In Fig. 162, let AB, BC, CD, etc., represent alternate trans- 
parent and opaque spaces constituting the ruling of a grating, of 
which the clear spaces are equal to one another, and so are the 




n ? m x n x o 

Fig. 162. Interference of Light by Diffraction. 

opaque. The total distance occupied by a clear and an opaque 
space is taken as the distance from line to line of the grating. 
Suppose monochromatic light to fall normally upon the grating. 
As the transmitted light falls upon a screen YZ, that from CD 
will reach a central region as O in the same phase as that from 
EF; the same is true of A B and G H, and O is light. At a certain 
distance from O, as at A r i, the light arriving from C by diffraction 
along C Ni travels a distance shorter than that from E along EN\ 
by the distance EK. This applies to the light from all points 
between C and D, as compared with that between E and F. If 
this difference in path, EK, is a half wave length, there will be 
interference in a limited space about JVi and therefore darkness. 
Further on, however, as at M\> where the difference between 



POLARIZATION 34 1 

CM\ and EM\ is a whole wave length, there will be light, suc- 
ceeded by interference at Ni where the difference in paths is 
three (or any odd number of) half wave lengths. A similar suc- 
cession of light and dark bands occurs on the other side of — 
light or dark according as the waves from C and E are in the same 
or opposite phases. They will be in the same phase if EN and 
C N differ by any integral number of wave lengths, i.e., if EK = n\ 

(or 2 n - J . They will be in opposite Dhases and produce inter- 
ference if EK = (2 n + 1) - • 

2 

If the distance CE is called d and the angular deviation NiLO 
is 0, EK = d sin 6. There will be light along YZ at the places 

where d sin 6 = 2 n - , and darkness where d sin 9 = (2 » + 1) -• 
2 2 

Since the regions along YZ, where violet light comes, are nearer 

the center than where red light comes, we see that the wave 

length of violet is less than that of red. Moreover, by measuring 

6 and knowing d, the value of X is calculable for any color. The 

construction applies equally to every point between A and B in 

connection with its corresponding point between C and D. 

By measuring the distances ONi and LNi, since — — - =sin 0, 

EN± 

we have, supposing Ni to be the first band of the color to be 

measured, from the center, 

EK X _ ON! 

EC d LNi 

Interference will be produced by reflection of light from two 
surfaces if the reflected waves differ in phase by half a period. 

Experiment No. g8, page 3 54. — Determination of wave length by means 
of a grating. 

245. Polarization. — If transverse waves of various lengths 
and periods were sent along a cord, and the cord itself were being 
rotated, the vibrations at one place would be horizontal, at 
another vertical, and elsewhere in any intermediate angular posi- 



342 



LIGHT 



tion. Not only so, but at any given point in the cord, the 
vibrations would not continue in one fixed direction. If such a 
line of vibrating particles could be viewed end-on, the vibratory 
motion at any instant within a limited length of the line would 
present a complex pattern. Fig. 746, Art. 113, is a simple 
example. 

Suppose the vibrating cord at one place passed between two 
boards; only the motion in the plane of the boards could be 
maintained, and beyond the boards the vibrations would be re- 
duced to motion in this plane. If, here, the cord had to pass 
between two other boards in a plane at right angles to that of 
the motion, the vibrations would be cut off (see Fig. 163a, b). 
(See also, Thomson, Light, Visible and Invisible, p. 114.) 




Fig. 163. Transmission and Interception of Waves. 

Something analogous to this occurs with light in passing 
through certain crystalline media, or undergoing reflection under 
certain conditions. 

In general, when action which is not limited as to its direction 
becomes restricted to some particular direction, this restriction 
is termed polarization, and the body or agent whose action is thus 
restricted is said to be polarized. Thus, a piece of iron or steel 



POLARIZATION 343 

becomes polarized by magnetization; a relay electromagnet is 
further polarized because its action is restricted to a current pass- 
ing in only one direction; light in which the vibrations are re- 
stricted in direction is polarized light. 

To continue the above illustration, if the vibrations were not 
those of a single line of particles, but presented to the barrier of 
boards a wave front of large width, polarization would occur by 
passing the vibrations through a pile of boards slightly separated, 
or even through a grating of parallel bars; a second grating with 
its plane parallel to the first and its bars in the same direction 
would not further impede the passage of the polarized waves, 
but if the second grating had its plane parallel to the first and its 
bars at right angles to those of the former it would intercept the 
vibrations polarized by the first grating. These two conditions 
are shown in the above Fig. 163 (a) and (b). 

The second grating permits the polarized waves to pass through 
it when it is in one position, but intercepts them when it is turned 
through an angle of ninety degrees. The first one of these two 
gratings is termed a polarizer and the second an analyzer, marked 
P and A, the purpose of the latter being to test whether waves 
through the first or any other medium are polarized. When the 
vibrations are reduced to one plane it is called plane polarization. 

When ordinary light falls obliquely upon a plate of glass, the 
light that is reflected and also that which is transmitted is partly 
polarized, and when examined with an analyzer the reflected 
fight is found to be polarized in a plane at right angles to that in 
which the transmitted light is polarized. By using a pile of a 
dozen or more thin plates, a larger portion of the light is reflected 
and the polarization of both the reflected and the transmitted 
portions is more marked. The angle of incidence for which the 
polarization is most nearly complete is the angle whose tangent 
equals the index of refraction of the substance. That is, for 
common glass with an index of refraction of 1.5 the incident ray 
should make an angle with the normal of about 56 , since the 
tangent of 56 is very nearly 1.5. In Fig. 164 is shown the result 
of such polarization. GG is the glass plate, the incident light is 



344 



LIGHT 




-H--T 



in the plane 10 N, perpendicular to the plane of GG, the incident 
ray making an angle ION of 56 . Suppose the plane of GG to 
be perpendicular to that of the paper, then the vibrations in the 
reflected ray OR 
are perpendicular 
to the plane of 
the paper, while 
those in the trans- 
mitted ray OT are 
parallel to the 
plane of the paper, 
but in each case 
transverse to the 
direction of prop- 
agation of the 
light. Those in 
10 are in all direc- 
tions in planes 
perpendicular to 
10. 

The mineral tourmaline has such a laminar structure that light 
passing through it is plane polarized, and a second crystal placed 
in the path of light that has passed through one such crystal 
transmits the light when in one position but extinguishes it when 
rotated through oo°. 

Polarized light, being simpler in its character than unpolarized, 
becomes a means of testing some physical or chemical proper- 
ties of bodies. For example, some substances, as mica, or a solu- 
tion of sugar, when placed in the path of a beam of polarized light, 
cause the plane of polarization to rotate through a certain angle. 
If light is passed through a polarizer and the analyzer is set so as 
to extinguish the light, and if then a cell containing a solution of 
sugar is inserted between the polarizer and the analyzer, the lat- 
ter no longer wholly cuts off the light but will do so when rotated 
through an angle depending on the nature of the substance in- 
serted and the thickness of it through which the polarized light 



Fig. 164. 



Polarization of Reflected and Transmitted 
Ray of Light. 



DOUBLE REFRACTION 



345 



passes. Not only so, but some substances cause rotation of the 
plane of polarization in one direction and others in the opposite 
direction. Thus cane sugar causes right hand rotation, while 
sugar from fruits produces left hand rotation. For an account 
of the many and beautiful phenomena of polarized light the 
student must refer to more extended works. 

The polarization of light was inexplicable until the adoption 
of the idea, due to Fresnel, that light waves are the result of trans- 
verse vibrations. 

246. Double Refraction. — Besides the means already men- 
tioned for the polarization of light, it is effected by the passage 
of light through any substance that causes double refraction. 




4&MM 



.".",■ 



(b) 



Fig. 165. Double Refraction by Iceland Spar. 

If a ray of ordinary light, as AR (Fig. 165a), falls upon the face 
of a crystal of calcite (Iceland spar), it is divided in its passage 
through the crystal, one portion, as RO, deviating in direction 
from AR by refraction at an angle whose sine bears a constant 
ratio to the sine of the angle of incidence. That is, it is refracted 
in the ordinary way and is called the ordinary ray. The other 
portion RE deviates from the direction AR by a different angle 
from that made by RO and usually lies in a different plane from 
ARO. The part RE is called the extraordinary ray. Its index 
of refraction is not constant but may range from zero to a maxi- 
mum value, depending on the nature of the crystal (which might 
be something other than calcite) and on the direction of the 



34 6 LIGHT 

incident light relatively to the principal axis of the crystal (to be 
explained below). This division of the ray is called double re- 
fraction, and both portions of the incident light, after emergence 
from the crystal, will give an image of the source of light, so that 
an object viewed through the crystal is seen double, and both 
the ordinary and the extraordinary ray are plane polarized, the 
vibrations in the one being at right angles to those in the other. 
Fig. 1655.) 

There is one direction in which light passes through the crystal 
without being thus divided. If the crystal were cut with all its 
edges equal and the natural angles retained, the equilateral 
rhomb thus formed would have two solid angles at opposite ends 
of a diagonal, each inclosed within three obtuse plane angles. 
The diagonal from one of these obtuse solid angles to the other 
is a principal axis, and any line parallel to this is an optic axis. 
Along this direction through the crystal, i.e., along any optic axis, 
the ordinary ray and the extraordinary ray coincide. 

A crystal of calcite may be divided and the two portions again 
cemented together with Canada balsam in such manner that the 
more refracted, i.e., the ordinary ray, meets the surface of the 
balsam at an angle so obtuse as to be totally reflected within 
the prism, while the extraordinary passes through, and thus the 
crystal transmits a beam of plane polarized light. The crystal 
so prepared is one of the most common and best forms of polarizer 
and is known as a Nicol's prism. It may be used either as a 
polarizer or an analyzer. (Exhibit.) 

The explanation of double refraction is an extension of that 
of single refraction. The latter is understood to be due to the 
fact that light is propagated at different velocities in the two 
media, Art. 228. Now the crystalline structure is probably such 
that light does not travel through it in all directions at the same 
rate. If light were examined as proceeding from any point 
within the crystal the progress along the ordinary ray in one 
plane would give a circular wave front, and since the velocity is 
constant for the ordinary ray, the complete wave front is spheri- 
cal, as in any isotropic medium. For the extraordinary ray, in 



FLUORESCENCE 347 

any one plane, the wave front is elliptical, and for all directions 
in the crystal the wave front is the surface of a spheroid. 

The larger proportion of transparent crystalline bodies, and 
any transparent substances not isotropic in structure, are double- 
refracting. This is notably so with glass in a state of strain. 
Light passing through such bodies is polarized, and when ex- 
amined with an analyzer displays beautiful color phenomena of 
interference, accompanying its transmission or extinction as the 
analyzer is rotated. 

Experiment No. gg, page 355. — Double refraction. 

247. Fluorescence. — The color of an object is determined by 
the light which it sends to the eye. If a translucent object is 
exposed to white light, a portion of the light will be transmitted, 
a portion will probably be absorbed (and its energy will thereby 
be transformed) and a portion will be reflected. 

If the object is viewed by the transmitted light it will have the 
color due to the wave lengths in the transmitted light; if it is 
viewed by reflected light, the wave lengths of the light reflected 
will determine its color. These may be different from those 
transmitted. 

There are some substances of such structure that light falling 
upon them produces, at the surface at least, a molecular vibra- 
tion of a period different from that of the incident light. Then, 
from the surface of the substance, light of a color different from 
the incident and the transmitted light proceeds. This emission 
of light of a period different from that causing it is termed fluores- 
cence. Most commonly the fluorescence is of longer waves than 
the exciting light. It occurs in many instances by exposing the 
fluorescent substance to the violet or ultra-violet part of the 
spectrum of white light. Thus, in this nearly or actually in- 
visible part of the spectrum of very short waves, objects may 
become visible, emitting light of greater wave length and of 
different colors according to their individual nature. The sub- 
stance absorbs the energy of the incident light and gives it out 
again in a lower order of vibration. But a given substance does 



34 8 LIGHT 

not so convert every order of radiation; it will fluoresce only in 
response to a certain portion of the spectrum. The effect is 
shown by viewing the substance by transmitted and then by 
reflected light. For example, petroleum of various degrees of 
refinement will transmit colors from a pale amber to deep red or 
dark brown, and reflect various tints of blue, or green, or pink. 
Experiment No. ioo, page 355. — Exhibition of fluorescence. 

248. Phosphorescence. — Closely related to the phenomenon 
of fluorescence is that of phosphorescence. After white light has 
illuminated certain substances, these glow in the dark, emitting 
light of a color (i.e., wave length), such as the substance, by selec- 
tive absorption from the incident light, is in condition to radiate. 
This property is most characteristic of the sulphides of calcium, 
barium and strontium, though it is shown to a less degree by 
many other substances. The phosphorescence continues in some 
of them for several hours before it quite dies out; in others it 
persists for only a few seconds. 

It is thought that fluorescence is in fact phosphorescence that 
lasts only a very brief length of time, perhaps only a minute 
fraction of a second. (See S. P. Thompson, Light; Visible and 
Invisible > pp. 174-176; The MacMillan Co.) 



EXPERIMENTS TO ILLUSTRATE CHAPTER VI. 



Experiment No. 8g, Art. 233. Total Reflection. 

Total reflection of light is beautifully shown by the "illuminated jet." A 

vessel 40 or 50 cm. high, as 
in Fig. 166, has an orifice 
at R about a centimeter in 
diameter, opposite to which, 
at id, is a lens that concen- 
trates upon R the light from 
the condenser L of the lan- 
tern. The vessel is filled with 
water, and when R is opened 
the light from L entering the 
jet illuminates it, but the light 
strikes the sides of the jet on 
the inner surface at so large 
an angle that it cannot emerge 
into the air but is continu- 
ously reflected internally. The 
whole curved jet is thus lumi- 
nous though the space about 
it is dark. A brilliant spot of 
light appears on the bottom of 
the vessel where the jet im- 
pinges. The effect is varied 
by inserting glass of various 
colors between L and A. 



A- 


R 


§taB!? 




ill. I'nlllllllll 









L -7T-. 



Fig. 166. Luminous Jet. 



Experiment No. go, Art. 23/. Reflection and Refraction. 

The optical disk is a circular disk against the face of which may be held 
sectional mirrors or lenses. At the edge of the disk is mounted a thin plate 
containing one or more slits through which light proceeds to the reflector 
or refractor, as shown in Fig. 167. 

Unless a beam of direct sunlight can be utilized, parallel light may be 
had by placing the projecting lens (objective) of the lantern in the path of 
the light from the lantern, at a distance from the focus to which the light is 

349 



35o 



LIGHT 





Fig. 167. The Optical Disk, illustrating various Phenomena of Reflection and 

Refraction. 



EXPERIMENTS 35 1 

brought by the condenser, equal to the focal length of the objective. With 
such a beam of light the optical disk shows all the principal phenomena of 
reflection and refraction. 

Experiment No. gi, Art. 238. Nos. gi and g2 illustrate Photometry. 

The Bunsen photometer has a spot, made by grease or melted paraffin, 
on a piece of white paper. With a light behind the paper the spot looks 
bright, with the light in front the spot looks dark; with a light behind and 
one in front at such relative distances as to illuminate the spot equally from 
both sides, the spot does not show in contrast with the paper, and then the 
lights are as the squares of their distances from the spot. 

Experiment No. g2, Art. 238. 

The Rumford photometer employs an opaque rod in front of a white 
surface, and the lights to be compared are placed so as to cast shadows of 
the rod beside each other on the white surface. The shadow from either 
light would be quite dark but for its illumination by the other light. When 
the lights are placed at such distances that the shadows are equally intense, 
these are equally illuminated, and the distance is measured from each light 
to the shadow it shines upon (not to the shadow it casts). The lights then 
are to each other as the squares of their respective distances from the surface 
they illuminate. 

Experiment No. g3, Art. 2^g. The Spectrum formed by a Prism. 

Project upon the screen the image of a narrow slit. Hold a prism of 
transparent substance against the outer face of the projecting lens, the 
edge of the prism parallel to the slit. The spectrum is formed by deviation 
of the light through a large angle toward the base of the prism. By turning 
the prism about an axis parallel to the slit, a position of the spectrum is 
found such that with further turning of the prism in either direction the 
spectrum moves so as to increase the deviation of the light. The prism is 
then in the position of minimum deviation. Prisms of various materials 
may be used, and of various angles, to show differences in refraction and 
dispersion. It will be found that with a glass prism of an angle of 90 the 
light entering one of the faces forming the right angle, perpendicularly, will 
not emerge through the hypotenuse upon which it strikes but be totally 
reflected from it as from a mirror, and emerge normally through the other 
face of the prism. 

Experiment No. g4, Art. 2^g. Continuous and Discontinuous Spectra. 

In a projecting lantern with an arc light, separate the carbons so as to 
make an arc, say, 6 mm. long. Remove the projecting lens and place an 



352 



LIGHT 



opaque card with a narrow horizontal slit at the focus of the arc as formed 
by the condenser. If the arc has been placed near the condenser its image 
will be considerably magnified, and the slit may be placed so as to receive 
upon it the image of the glowing positive carbon, as at Si (Fig. i68), and ac- 
cordingly be illuminated by an incandescent solid. Project the image of 



Violet 




Red 



Fig. 1 68. Projection of Spectrum. (The enlarged carbons and arc represent 
simply the image of the real carbons and arc, at the left.) 



the slit upon the screen by the lens L. By placing the prism P in the light 
immediately beyond L, the spectrum is shown on the screen in vertical 
position ranging continuously from red to violet. 

1 If the slit be raised so as to receive upon it the image of the arc, as at S 2 , 
it is illuminated by the luminous gas between the carbons, and when L and 
P are again adjusted so as to form the spectrum from 5*2 upon the screen, this 
is found to consist of bands of various colors intermitted by dark spaces 
between them. They are separate images of the slit, and the spectrum is 
discontinuous. If a carbon is employed such as is used for the flaming arc 
lights, the spectrum of the salts with which the carbon is impregnated is 
shown in brilliant bands from the arc, but the spectrum of the solid is still 
seen to be continuous. 

Experiment No. Qj, Art. 226 and Art. 24 j. 

Newton's Rings may be shown in light from any source with the usual 
combination of plane and curved glasses clamped together. They may be 
projected by placing them near the focus of the lantern condenser, as in 
Fig. 169, and then focusing the contact spot S in the reflected light, so as 
to produce the image of the rings upon the screen as at /. It is best to have 
a black paper or cloth behind the glass, at B. 



EXPERIMENTS 



353 



Experiment No. g6, Art. 24 j. Monochromatic Light. 
The spectrum of sodium vapor illuminating a slit 2 or 3 mm. in width 
is a single band of yellow; if the slit is very narrow the spectrum is two 
yellow strips slightly sepa- 
rated. The light of sodi- 
um, then, is only yellow 
and is one of the best ex- 
amples of monochromatic 
light. If a strip of asbes- 
tos packing, or even ordinary cloth, is wrapped around the 
upper part of a Bunsen burner so as to project a little way 
above the top of the burner, and is soaked in salt water, 
the flame of the burner will give a strong yellow sodium 
light. In light of any one color, objects will appear either 
of that color or none. In the sodium light everything is 
black or of a pallid hue; objects of various bright colors 
will all look black except in so far as yellow is a con- 
stituent in their color. If not black, therefore, they will 
range through various tints from a pale to a bright yellow. 
The complexion of the lecturer and of the spectators has a 
ghastly hue. 

Experiment No. 97, Art. 243. Interference Bands. 

Obtain two pieces of plate glass, 8 or 10 cm. square, as 
nearly plane as possible. Lay them on a black paper or 
cloth, the one fitting snugly upon the other. Around the 
top of a Bunsen burner wrap a strip of asbestos packing 
that has been soaked in salt water. The gas from the v2E~2> 
burner will then give a strong yellow flame that is the light p- 6 p ro _ 
of sodium and is virtually monochromatic. jection of New- 

Its reflection from the glass surfaces on the table shows ton's Rings, 
brilliant bands of yellow and black, straight and uniform if 
the surfaces are plane, or varying in figure according to the irregularity in 
thickness of the air film between the glass surfaces. Pressing the glasses 
together makes the film thinner and the bands correspondingly broader. 
In this, as in all experiments with light of diminished intensity, the effect 
is better the darker the room. 

To project this, remove the objective and prop the lantern in an inclined 
position so that the light from the condenser falls upon the plates on the 
table at a large angle to the normal. Place the objective or any projecting 
lens in the reflected light and focus the plates on the screen. If the con- 
tact between the plates is sufficiently close the bands will appear in various 
colors from ordinary light. 



354 



LIGHT 



In this, however, as in many other special cases of projecting, the ob- 
jective of the lantern fails to utilize a good deal of the light that is available, 
and all is needed that can be had. A convex lens 4 or 5 inches in diameter, 
such as is sold by opticians as a reading glass, can readily be clamped in any 
position, and will often serve better than the regular lantern objective. 

The effect in this experiment is improved by using monochromatic light. 
If the lantern has an arc lamp, a fairly good sodium light can be obtained 
by drilling out the core of one carbon to a depth of about 2 cm. and packing 
the bore full of fine salt. Make this the lower carbon, and preferably the 
positive. Then with a moderately long arc the light is chiefly yellow, and 
the interference bands are yellow and black. , 

Experiment No. 98, Art. 244. Measurement of Wave Length of Light by 
Means of a Grating. 

If the light falling upon the grating comes from an illuminated slit, as 
in Fig. 170, which is projected upon the screen YZ, then by placing a 




R V 



Fig. 170. Spectrum formed by a Grating. 



transmission grating ruled with several thousand lines to the inch in front 
of the projecting lens at D, there will be a white image of the slit at 0, con- 
taining most of the light passing through the grating, with a series of spectra 
on each side, that are the colored images resulting from diffraction. If \ v 
is the wave length of violet light, and d the distance between the lines of 
the grating, measure OV and DV; then 



d 



ov_ 

DV' 



or X, 



d 



OV 
DV 



EXPERIMENTS 355 

and the wave length for any other part of the spectrum may be determined 
in the same manner. 

Experiment No. gg, Art. 246. Double Refraction. 

In the slide holder of the lantern place a card or opaque plate with an 
orifice about 2 mm. in diameter. Focus this on the screen and place a 
crystal of calcite before the orifice; the image of the orifice on the screen is 
double. Rotate the crystal and observe the displacement of the images. 
When the direction of the light through the crystal coincides with the optic 
axis, only one image is seen. 

Experiment No. 100, Art. 24J. Fluorescence. 

In a well darkened room project as bright a spectrum as possible. In 
various parts of the spectrum place fluorescent substances as described 
below and observe their color. 

(a) A dilute solution of sulphate of quinine in water slightly acidulated 
with sulphuric acid is colorless by transmitted light, but is a rich blue in 
the ultra-violet part of the spectrum, and in nearly every color of the spec- 
trum. 

(b) Green leaves thoroughly macerated in ether or alcohol give a green 
solution of chlorophyl that is red when placed in violet light, and in the 
other parts of the spectrum except the extreme red. 

(c) Eosin (a few drops of red ink will answer), in water, produces a red 
solution that fluoresces. 

(d) A solution of thallene shows a rich green in all parts of the spectrum 
beyond the yellow on the violet side. 

(e) Petroleum, showing yellow or brown by transmitted light, fluoresces 
blue or green. 

These may all be exhibited by placing them in ordinary test tubes and 
holding them in the path of the light forming the spectrum. (For prepara- 
tion and exhibition of these substances, see Light, by Lewis Wright, Mac- 
millan Co.) 



356 



TABLE OF PHYSICAL DATA 



PHYSICAL DATA FOR 

For quantities of variable values a mean is given. Where possible the figures are correct to within 
upon temperature and pressure, the figures are for 0° C, and 76 cm. barometer pressure unless 
generally accepted as authoritative. 



Aluminum 
Beeswax 
Brass . . 
Carbon, 

diamond 
Carbon. 

graphite 
Catgut. . . 
Copper. . . 

Cork 

Glass, 

crown 
Glass, 

flint 
Gold. . . 
Ice .... 
India 

rubber 
Iron .... 
Lead. . . . 
Paraffin . 
Platinum 
Silver . . . 
Sulphur . 

Tin 

Zinc .... 



Specific 
Gravity, 
Density, 
Grams 
per cc, 
Water at 
4° C. = i. 



2.65 
.95 

8.4 

3.51 

2.25 
1.5 
8.94 
.24 



2.9-4.5 
19.32 

.916 

.94 

7.86 

11.36 

.88 

21.5 

10.57 

2.07 

7.29 

7.1 



Elasticity; 

Dynes per 

Sq.cm. For 

Solids, 
Young's Mod- 
ulus; for 
Fluids, Bulk 
Modulus. 



7.05X10" 
10.0 



.31 
12.3 



7.0 



Melting 
Point, ° C, 



8.0 



.05 
21.0 
1.62 



16.8 
7.9 



5.43 
9.0 



657 
62 



1050 



1250 




1600 
325 

52.4 
1700 



115 
231 
420 



Boiling 

Point, 

C. 



Specific 

Heat, 
Cals. per 
Gm. per 
Degree C. 



1470 



440 
930 



.202 
.094 



095 



0324 
5 



112 
,032 
.694 
.03 



.184 
.056 
,CC4 



Coefficient 

of Expan- 
sion per 

Degree C; 

Linear for 
Solids; 
Cubical 

for Fluids. 



. C0C0222 

.0000189 



.0000167 



CCC0089 



0000142 
0000510 



.0000121 
.0000280 

, C0000S7 

.0000641 
.0000214 

.CC0C29S 



TABLE OF PHYSICAL DATA 357 

VARIOUS COMMON SUBSTANCES 

one-tenth of one per cent; in most instances, to a higher degree of accuracy. For vaiues depending 
otherwise stated. Compiled from Landolt and Bornstein, Smithsonian, and other tables that are 



Thermal 
Conductiv- 
ity, Cals. 
per Sec. 
through a 
Plate i 
Sq.cm. 
Cross-sec- 
tion, i Cm. 
Long; i°C. 
Dif. in 
Temp, 
between 
Ends. 



.48 



20 



92 
00072 

0017 



75 
004 



161 

084 



166 



152 
265 



Latent 
Heat of 
Fusion; 
Calories 
per Gram. 



76. S 
42.3 



42.0 



5.9 
35.1 

27.2 

9.37 
14.0 
28.13 



Velocity of 

Sound: in 

Solids and 

Liquids, 

Elasticity 



Cp Pressure 



Cv Density 
Meters per 
Sec. 



5160 
3460 



1460 
3710 



5292 



2035 



730 
5170 
1195 

2796 



2728 
3560 



Liberated 
from Solu- 
tion by 
Current of 
i Ampere, 
Grams per 
Second. 



.000094 



.000329 



.000681 



.001012 
.001118 



000339 



Sp. Resist., 

Resistance of 

Conductor 

i Sq.cm. 

Cross- section, 

i Cm. Long, 

Ohms. 



2.67X10- 6 

8.5 

3000. 
1.6 



2.2 



10.0 
20.0 

11.0 
1.47 

11.0 



Refractive 
Index of 
Light for 
Mean D 

Line; into 

Solids and 
Liquids 

from Air; 

into Gases 

from 

Vacuum. 



2.42 



0.641 



1.5 

1.58-1.9 
0.366 
1.31 



2.06 



E.M.F. of 

Battery 

Cells, Volts. 



Clark 
Standard 
1.434 

Daniell (or 
gravity), 
1.08 

Dry, 1.5 + 

Leclanche, 
(sal ammo- 
niac), 1.48 

Weston 
Standard 
1.018 

Storage, 
lead plates 
2.2 

Storage, 
Edison, 
(iron-nickel), 
1.1 



358 



TABLE OF PHYSICAL DATA 



PHYSICAL DATA FOR VARIOUS 

For quantities of variable values a mean is given. Where possible the figures are correct to within 
upon temperature and pressure, the figures are for o° C, and 76 cm. barometer pressure unless 
generally accepted as authoritative. 





Specific 
Gravity, 
Density, 
Grams 
per cc, 
Water at 
4° C. = i. 


Elasticity; 

Dynes per 

Sq.cm. For 

Solids, 
Young's Mod- 
ulus; for 
Fluids, Bulk 
Modulus. 


Melting 
Point, ° C. 


Boiling 

Point, 

C. 


Specific 

Heat, 
Cals. per 
Gm. per 
Degree C. 


Coefficient 

of Expan- 
sion per 

Degree C; 

Linear for 
Solids; 
Cubical 

for Fluids. 


Thermal 
Conductiv- 
ity, Cals. 
per Sec. 
through a 
Plate 1 
Sq.cm. 
Cross-sec- 
tion, 1 Cm. 
Long; i° C. 
Dif. in 
Temp, 
between 
Ends. 


Alcohol, 1 

ethyl / 

Alcohol, 1 

methyl J 


.792 


.1031X10" 




78.3 


.615 


.00108 


.00043 


.810 






66.3 


.613 


.00136 








Carbon di- 


1.292 






46.1 


.24 




.00034 


sulphide 
















Ether 


736 






35 5 


.517 


00163 




Glycerine 
Mercury . . 


1 26 






290 


.576 


00053 


.00068 


13.596 


5.415 


-39 


356 


.0335 


.00018 


.015 




92 














Turpentine 
Water. ... 


87 






156 


407 


00105 


0003 


.9998 


.2045 




100 


1 at 15° C. 


.00013 


.0014 


Air 


.001293 






-191 | 


C p , .237 
C P , .168 


| .00367 


.000052 


Ammonia 


.000771 




- 75 


-38. 5 








Carbon di- 
oxide 
Chlorine.. 


.001977 
.00317 


For gases, 

elasticity 

isothermally 


-102 • 


-78.2 | 
-33. c[ 


C p , .217 
C V} .172 
C p , .121 
C v , .093 


} 

} 


.000032 


Hydrogen 


.0000899 


equals the 
pressure; 


-257 


-253 | 


C p , 3.409 
C v , 2 All 


j .00367 


.00032 


Nitrogen . 


.001251 


adiabatically, 


-210 


-195 | 


Cp, .244 
C v , . 173 


j .00367 


.000052 


Oxygen . . 


.001429 


— X pressure. 


-227 


-182 | 


Cp, .218 
C v , .155 


} .00367 


.000056 


Steam.. . . 
(100°) 


. 000596 






{ 


C p , .481 
C v , .37 


} 





TABLE OF PHYSICAL DATA 



359 



COMMON SUBSTANCES— Continued 

one-tenth of one percent; in most instances, to a higher degree of accuracy. For values depending 
otherwise stated. Compiled from Landolt and Bornstein, Smithsonian, and other tables that are 



Latent 
Heat of 

Vaporiza- 
tion, at 

Temp, of 
Boiling 


Maximum 
(Saturation) 
Pressure of 
Vapor in 
Mm. of 
Mercury 
Column. 


Velocity of 

Sound; in 

Solids and 

Liquids, 

^ /Elasticity 

' Density 
in Gases, 


Liberated 
from Solu- 
tion by 
Current of 
i Ampere, 
Grams per 
Second. 


Refractive 
Index of 
Light for 
Mean D 

Line; into 

Solids and 

Liquids 
from Air; 

into Gases 

from 
Vacuum. 


Wave Length of Radiation; Cms. 


Solar Spectrum. (End of One Color 
is Beginning of Next.) 


Point, 


\Cj) Pressure 


per Gram. 


* Co Density 

Meters per 

Sec. 




f 


0°, 12.7° 


] 






Ultra violet, beginning, 


2948 X 10~ 8 


202. \ 


20°, 44.5 


\ 1149 




1 . 369 


Violet, beginning 


3970 


78°.3, 760 


J 






Indigo, beginning 


4240 












Blue, beginning 


4550 


S3. 8 


127.9 
0°, 18.4 
20°, 432.8 
35°.5, 760 






1.643 
1.357 


Green, beginning 
Yellow, beginning 
Orange, beginning 
Red, beginning 


4920 


f 
90.0 \ 


1 


5750 
5850 
6470' 








1.47 
1.73 
1 476 


Infra red, beginning 
Infra red, ending 
Sodium flame: 


8100 


62.0 


.004 


2020 


27000 


69.0 


2.1 

-5°, 3.13 

0°, 4.6 

10°, 9.17 

20°, 17.39 

50°, 91.98 

100°, 760 






1.47 


mean D line 

X-rays 
Wireless telegraphy 
Fraunhofer lines, cms. 


5893 






1 

100-5()00m 


536.0 


• 1432 




1.333 


A, Oxygen, dark red 


7594 XI 0~ 8 










B, Oxygen, dark red 


6867 










C, Hydrogen, red 


6563 










Di, Sodium, orange 


5896 












D z , Sodium, orange 


5890 


51. 




331.2 




1 . 000292 


E, Iron, green 


5270 


2.95 








1.000377 


F, Hydrogen blue 

G, Iron, indigo 


4861 






4308 


86.7 




200.0 






H, Calcium, violet 


3968 


67.0 




212.0 


.000368 


1.000768 






200.0 




1268.0 


.0000104 


1.000138 






48.0 




337.8 




1.000297 






51.0 




315.0 


.0000832 


1.000272 







INDEX. 



(Numerals refer to pages.) 



c. 



Aberration, chromatic, $36. 

of light, 310. 

spherical, 330. 
Absolute measurements, 9. 

units, 23. 

zero, 108. 
Acceleration, 22. 

central, 34. 
Accommodation of the eye, 331. 
Achromatic lens, 337. 
Activity, 242. 
Adiabatic curves, 142. 
Air pumps, 75. 
Ammeter, 253. 
Ampere, 237, 246. 
Apparent depth of a transparent 

medium, 322. 
Archimedes' principle, 56. 
Arc light, 259. 

Aspirating action of flow, 76. 
Atmospheric conditions that affect 

comfort, 135. 
Atmospheric pressure, 70. 
Audition, limits of, 197. 
Avogadro's law, 109. 

B. 

Barometers, 71. 

Battery, joining cells to form a, 284. 

Beats, 196. 

Bolometer, 251. 

Boyle's law, 72. 

deviations from, 73. 
Brownian movement, 84. 
Buoyancy, 56. 

of the air, 133. 



Calorie, in. 
Calorimetry, in. 
Candle, standard, 333. 
Capacity, for electricity, 221. 

for heat, in. 

of a sphere, 228. 
Capillarity, 67. 
Cartesian diver, 93. 
Cathode rays, 289. 
Cavendish experiment, 42. 
Center, of gravity, 45. 

of percussion, 55. 

of pressure, 54. 
Centrifugal force, illustrated, 89. 
Circuit, divided, 247. 

electric, 233. 
Colors of thin plates, 339. 
Combination tones, 196. 
Concurrent forces, 88. 
Conduction of heat, 136. 
Conductivity, electrical, 241. 

thermal, 136. 
Constant, Regnault's, no. 

solar, 146. 
Constants of nature, 38. 
Contraction of liquids on mixing, 

52. 
Convection, 138. 
Corti's fibers, 190. 
Coulomb, unit of electricity, 240. 
Couple, 43. 
Critical angle, 320. 

pressure, 118. 

temperature of a gas, 125. 
Crookes' layer, 128. 
Crookes' tube, 286-288. 
Culinary paradox, 122. 



361 



362 



INDEX 



(Numerals refer to pages.) 



Current, chemical effect of, 278. 

electricity, 232. 

sheet, 252. 
Currents, attraction and repulsion of, 

258. 
displacement, 284. 

D. 

Dalton's laws, 119. 

Density, determination of, 62. 

meaning of, 61. 
Detectors in wireless telegraphy, 287. 
Dew point, 131. 
Diffraction, 340. 
Diffusion, 82. . 
Dispersion of light, 335. 
Displacement of currents, 284. 
Doppler's principle, 179. 
Double refraction, 345. 
Dynamics, significance of, 6. 
Dynamo, the electric, 271. 

three types of winding, 273. 
Dye, unit of force, 23. 

E. 

Ebullition, 121. 
Efflux, velocity of, 75. 
Elasticity, 53. 

of a gas at constant temperature, 74 
Electric actions summarized, 294. 
Electrical force inside of a conductor, 

228. 
Electric, capacity of a sphere, 228. 

circuit, 233. 

condenser, 224. 

field of force, 220. 

lighting, systems of, 260. 

lights, 258. 

lines of force, 226. 

potential, 260. 

resistance, 241. 
Electricity, capacity for, 221. 

discharge of, through gases, 287. 

static, 219. 

unit of, 220. 



Electrification, two kinds of, 219. 

by induction, 222. 
Electrokinetics, 232. 
Electrolysis, 278. 
Electromagnets, 266. 
Electrometers, 230. 
Electromotive force, 233. 

sources of, 234. 
Electron, 290. 

theory of electricity, 293. 
Electrophorus, 223. 

Energy, conservation and correlation 
of, 28. 

distribution of, in an electric field, 
229. 

forms of, 31. 

of electric charge, 225. 

potential, tends to a minimum, 46. 
Entities of nature, 6. 
EquipQtential surface, 210. 
" Eureka," story of, 59. 
Experiments to illustrate: 

Archimedes' principle, 92. 

atmospheric pressure, 98. 

attraction and repulsion of currents, 
301. 

beats, 206. 

bodies falling in a vacuum, 90. 

bodies rolling up hill, 91. 

boiling point dependent on pressure ; 

151- 
capacity for heat, 149. 
capillarity, 96. 
Cartesian diver, 93. 
centrifugal force, 89. 
concurrent forces, 88. 
conduction of heat, 152. 
cork submerged under mercury, 94= 
cycle of energy changes, 303. 
determination of density, 94. 
determination of g, by Galileo, 91. 

by helical spring, 90. 
diffusion, 99. 
double refraction, 355. 
electric conductivity of liquids, 300. 
electrification by induction, 297. 



INDEX 



363 



(Numerals refer to pages.) 



Experiments to illustrate: 
electrophorus, 304. 
exchange of liquids between two 

vessels, 95. 
expansion and contraction, 147. 
expansive force of a gas, 97. 
fluorescence, 355. 
forces and displacement, 92. 
freezing by evaporation, 151. 
independent action of simultaneous 

forces, 88. 
induction in earth's magnetic field, 

296. 
inertia, 85. 

interference of waves, 168. 
of light, 353. 
of sound, 203. 
Kundt'sdust figures, 202. 
law of magnetic force, 296. 
lines of flow in a current sheet, 

304- 
localization of energy in a conduc- 
tor, 300. 
magnetic field around a conductor 

carrying a current, 299. 
magnetic induction of currents, 302. 
magnetic lines of force, 296. 
manometric flames, 201. 
measurement of wave length of light, 

354- 
Newton's rings, 352. 
Oersted's experiment, 300. 
osmotic pressure, 98. 
overtones, 201. 
photometry, 351. 
pitch, determination of, 200. 
polarization and depolarization, 305. 
reflection and refraction, 349. 
regelation, 149. 
resonance, 202. 

rigidity, conferred by motion, 86. 
rotation of the earth (Foucault), 

86. 
self-induction, 303. 
sensitive flames, 199. 
singing flame, 199. 



Experiments to illustrate: 

sound not transmitted in a vacuum, 

159. 
sound vs. noise, 199. 
sound wave, movement of, 200. 
spectrum, by a prism, 351. 
continuous and discontinuous, 

^Si- 
stationary waves, 168. 
surface tension, 95. 
sympathetic vibration, 203. 
test tube falling upward, 94. 
thermoelectric current, 303. 
total reflection, 349. 
typical wave forms, 168. 
vapor pressure, 150. 
vibration of strings, 205. 
vortex motion, 85. 
External action of charged sphere, 
228. 



F. 



Fahrenheit, Daniel Gabriel, 102. 
Farad, practical unit of capacity, 240, 

244. 
Faraday's law of electrolysis, 279. 
Field of force, 207. 

about a conductor, 235. 
Fizeau's method of determining veloc- 
ity of light, 308. 
Fluid, definition of, 11. 

pressure, 53. 
Fluorescence, $^8. 
Foci, conjugate, 324. 
Focus, principal, 324. 
Force, centrifugal, centripetal, 35. 

field of, 207. 

line of, 207. 

measure of, 23. 

nature of, 13. 

of a blow, 22. 

of inertia, 19. 
Forces, composition of, 20. 

parallelogram of, 25. 

resolution of, 20. 



364 



INDEX 



(Numerals refer to pages.) 



Foucault's method of determining the 

velocity of light, 309. 
Foucault's pendulum experiment, 86. 
Freezing — a warming process, 1 14. 
Friction, 48. 
Fundamental ideas, 2. 
Fuse plug, 260. 
Fusion, latent heat of, 113. 
laws of, 115. 



Galvanometer, D'Arsonval, 239. 

moving coil, 239. 

tangent, 237. 
Gas, constant, no. 

definition of, ri. 
Geissler's tube, 288. 
Gram molecule, 294. 
Gravitation, fall of bodies, 40. 

universal law of, 41. 
Gravity, center of, 45. 

constant, 42. 

determination of, 39. 

specific, 58. 
Gridiron pendulum, 104. 



Impulse, 22. 

Index of refraction, 314. 

Induced currents, 262. 

direction of, 266. 

E.M.F., 265. 
Induction coil, the, 273. 

tubes of, 227. 
Inertia, force of, 19. 

law of, 15. 

moment of, 49. 

time element in, 85. 
Intensity of sound, 181. 
Interference, of light, 3380 

of sound, 185. 

of waves, 162. 
Intervals in music, 177. 
Ions, liberation of, 279. 

migration of, 281. 
Isothermal curve, 142. 

j- 

Joule, James Prescott, 144. 
Joule, unit of energy, 242. 
Joule's law, 257. 



H. 

Heat, dynamical equivalent of, 143. 

mechanical equivalent of, deter- 
mined electrically, 258. 

nature of, 105. 

sources of, 145. 

specific, in. 

transference of, 136. 
Heating action of a current, 257. 
Hiero's crown, 59. 
Hooke's law, 53. 
Horror vacui, 71. 
Humidity, determination of, 131. 

meaning of, 130. 
Hygrometry, 130. 

I. 

Images, formed by lenses, 328. 
real and virtual, 317, 



K. 

Kinetic energy, 54. 

theory of matter, 79. 
Kundt's tube, 185. 

L. 

Latent heat, of fusion, 113. 

of vaporization, 123. 
Law, of gravitation, 41. 

of motion, first, 17. 

of motion, second, 19. 

of motion, third, 26. 

physical, 9. 
Laws of thermodynamics, 143, 
Lenses, power of, 330. 
Lenz'slaw, 262. 
Leyden jar, 224. 
Light, aberration of, 307. 



INDEX 



365 



(Numerals 

Light, electromagnetic theory of, 312. 

interference of, 338. 

invisible, 316. 

nature of, 306. 

velocity of, methods of determin- 
ing, 306. 
Lines of force, physical interpreta- 
tion of, 216. 
Liquefaction of a gas, 126. 
Liquid, definition of, 11. 

pressure of a, 53. 
Localizing work in a circuit, 258. 
Lux, unit of illumination, 334. 

M. 

Magdeburg hemispheres, 70. 
Magnetic phenomena and definitions, 

213. 
Magnetic substances, 217. 
Magnetism, terrestrial, 218. 
Magnetization by induction, 217. 
Mariotte's flask, 78. 
Materials, properties of, Table, 356. 
Matter, 5. 

forms of, n. 

kinetic theory of, 79. 

nature and properties of, 10 

properties of, 52. 
Mechanical equivalent of heat, 143. 
Mechanical powers, 47. 
Mechanics, 32. 
Melting point, 115. 

influence of pressure on, 116. 
Molecules, mean velocity of, 81. 
Moment of a force, 48. 

of inertia, 49. 
Momentum, 22. 
Motion, laws of, 17, 19, 26. 

simple harmonic, 35. 
Motor, the electric, 272. 
Musical instruments, 197. 
Musical scale, 177. 

N. 

Natural scale, 177. 
Nature, constants of, 38. 



refer to pages.) 

Nature, pitch of, 188. 
Nernst lamp, 262. 
Newton's rings, 338. 
Nitrogen lamp bulb, 259. 

O. 

Ohm, the, 242, 244. 

Ohm's law, 241. 

Optical center of a lens, 329. 

Optics, geometrical and physical, 316. 

Osmosis, 83. 

Osmotic pressure, 84. 

Overtones, 182. 

P. 

Pascal's principle, 53. 
Pendulum, simple, 37. 
Phase of reflected waves, 161. 
Phosphorescence, 348. 
Photometry, 332. 
Physics, definition of, 8. 

ways of viewing, 1. 

why study? 2. - 
Pitch, 175. 

of nature, 188. 

standard, 179. 
Pneumatics, 70. 
Polarization, of electrolytic cell, 282. 

of light, 341. 
Porosity, 52. 
Potential, application of, 214. 

difference of, 209. 

measure of, 211. 

theory of, 207. 
Poundal, unit of force, 23. 
Power, 242. 

Powers, mechanical, 46. 
Practical units, 242. 
Pressure, center of, 53. 

critical, 118. 

effect of, on melting point, 116. 

effect of, on boiling point, 121. 

of a fluid, 53. 

of a liquid, 53. 

of the atmosphere, 70. 



3 66 



INDEX 



(Numerals refer to pages.) 



Pressure, on submerged surface, 53. 

osmotic, 84. 
Properties of materials, table of. 356. 
Principle of Archimedes, 56. 
Psychrometer, 128, 134. 
Pumps, 79. 

Q- 

Quality of sound, 182. 

R. 

Radiation, 139. 
Radioactivity, 291. 

Rate of travel, of longitudinal waves, 
166. 

of transverse waves, 165. 

of water waves, 164. 
Rays of light, 306. 
Rays, Rontgen or X, 290. 
Reflection and refraction of light, 313. 
Refraction through plate with par- 
allel sides, 328. 
Refractive index, 314. 
Regelation, 117. 
Resistance, coils, 247. 

how to measure, 249. 

specific, 245. 

unit of, 241. 

variation of, with temperature, 245. 
Resonance, 186. 

Rigidity conferred by motion, 86. 
Ripples, 165. 
Rolling pin model, 91. 
Rontgen rays, 290. 
Rotation, energy of, 49. 

of the earth, 19. 
Rumford, Count, 107. 



Science and measurement, 8. 
Seeing of objects, the, 316. 
Selective absorption, 190. 
Self-induction, 268. 
Sensitive flame, 199. 
Shunts, 248. 



Simple harmonic motion, 35. 
Simple pendulum, 37. 
Simultaneous forces, 87. 
Siphon, simple, 77. 

intermitting, 77. 
Solar constant, 146. 
Solenoid, magnetic field in a, 266. 

strength of field in a, 266. 
Solid, definition of, 11. 
Sound and noise distinguished, 171. 
Sound, a wave phenomenon, 170. 

due to longitudinal vibration, 1710 

intensity of, 181. 

phenomena, complexity of, 171. 

quality of, 182. 

reflection and interference of, 182. 

three characteristics of, 175. 

velocity of, 172. 
Space, 3. 

Specific, density, 61. 

gravity, 58. 

heat, in. 
Specific, heats of a gas, two, 114, 
Spectroscope, direct vision, 337. 
Spectrum, the, 335. 
Spheroidal state, 1 26. 
Spinthariscope, 292. 
Springs, intermittent, 77. 
Stage recitation, 1 79. 
Standard candle, ^33- 
Storage battery, the, 283. 
Strength of field, 208. 
Stress, 12. 

Submarine boat, Holland, 91. 
Surface tension, 64. 
Sympathetic vibration, 190. 



T. 



Table of properties of materials, 356. 
Tantalus' vase, 77. 
Telephone, the, and telegraph, 276. 
Temperature, 100. 

measured by variation in electric 
resistance, 251. 

scales, 101. 



INDEX 



367 



(Numerals refer to pages.) 



Tempered scale, 178. 

Thermodynamics, laws of, 143. 

Thermoelectricity, 277. 

Thermometer scales, 101. 

Thermos bottle, 141. 

Time, 3. 

Total reflection, 320. 

Transformers, 275. 

Tubes of force, 226. 

Tyndall, Professor, 107, 119, 144. 

U. 

Unit, capacity, 240. 

current denned, 237. 

difference of potential, 240. 

of heat, in. 

of light and of illumination, 334. 

quantity of electricity, 240. 

resistance, 241. 
Units, 9. 

choice of, 234. 

international, 243. 

practical, 242. 

principal dynamic, 32, 

V. 

Vacuum bulb (Dewar's), 141. 
Van der Waal's equation, 128. 
Vaporization, 119. 

latent heat of, 123. 
Vapors, elastic force of, 119. 
Velocity, 21. 

of efflux, 75. 

of molecules, 81. 

of propagation of waves, 1 59. 

of sound, 172. 

effect of temperature on, 174. 
independent of pitch, 180. 
Laplace's correction for, 174. 
Vibration, of air in pipes, 191. 

of rods, longitudinal, 182. 

- f strings, 193. 



Vibration, sympathetic, 190. 

Vibratory motion and wave forms, 155. 

Virial, Clausius' equation of the, 129. 

Vision, defects of, 331. 

Voltaic cell, the, 282. 

Voltameter, 281. 

Volt, the practical unit of E.M.F., 240, 

244. 
Voltmeter, 254. 
Vortex rings, formation of, 85. 

W. 

Water, anomalous behavior of, 106 

maximum density of, 106. 
Watt, unit of activity, 242. 
Wattmeter, 256. 
Weston normal cell, 283. 
Wave apparatus, Columbia, 157. 

Lyman's, 156. 
Wave, forms, 155. 

front, 159. 

length of light, measurement of, 237. 

rate of travel of a, 164. 

theories, 154. 
Waves, and rays, 312. 

interference of, 162. 

reflected, phase of, 163. 

reflection of, 160. 

stationary, 161. 

velocity of propagation of, 159. 
Weighing the earth, 44. 
Wheatstone bridge, 249. 
Wireless telegraphy, 286. 
Work, and energy, 27. 

internal and external, 124. 

of expansion, no. 



X. 



X rays, 290. 



Zero, absolute, 108. 



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Baker, T. T. Telegraphic Transmission of Photographs i2mo, 

(Reprinting.) 
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Vol. I. Foundry Equipment, Materials Used *3 00 

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Ball, R. S. Popular Guide to the Heavens 4 8vo, 

1 Natural Sources of Power 8vo, 

Ball, W. V. Law Affecting Engineers 8vo, 

Bankson, Lloyd. Slide Valve Diagrams i6mo, 

Barham, G. B. Development of the Incandescent Electric Lamp..8vo, 

Barker, A. F. Textiles and Their Manufacture 8vo, 

Barker, A. F., and Midgley, E. Analysis of Woven Fabrics 8vo, 

Barker, A. H. Graphic Methods of Engine Design i2mo, 

Heating and Ventilation 4to, 

Barnard, J. H. The Naval Militiaman's Guide i6mo, leather 

Barnard, Major J. G. Rotary Motion i6mo, 

Barnes, J. B. Elements of Military Sketching i6mo. 

Barnett, E. deB. Coal-Tar Dyes and Intermediates 8vo, 

Explosives 8vo, 

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Barrowcliff, M., and Carr, F. H. Organic Medicinal Chemicals. .8vo, 

(In Press.) 



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4 D. VAN NOSTRAND CO.'S 'SHORT ? TITLE CATALOG 

Barrus, G. H. Engine Tests. ...... .8vp, 

Baterden, J. R. Timber jj V0> 

Bates, E. L., and Charlesworth, F. Practical Mathematics and 
Geometry , I2mo> 

Part I. Preliminary Course 100 

Part II. Elementary Course .:. 100 

Part III. Advanced Course 1 50 

Practical Mathematics i 2 mo, 

— — Practical Geometry and Graphics i2mo, 

Batey, J. The Science of Works Management i2mo, 

Steam Boilers and Combustion i2mo, 

Bayonet Training Manual i6mo, 

Beadle, C. Chapters on Papermaking. Five Volumes 12010, each, 

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Finishing of Textile Fabrics 8vo, 

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Beaumont, W. W. The Steam-Engine Indicator 8vo, 

Bechhold, H< Colloids in Biology and Medicine 8vo, 

Beckwith, A. Pottery 8vo, paper, 

Bedell, F. The Airplane 8vo, 

Bedell, F., and Pierce, C. A. Direct and Alternating Current Manual. 

8vo, 

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Beggs, G. E. Stresses in Railway Girders and Bridges {In Press.) 

Begtrup, T. The Slide Valve 8vo, 

Bender, C. E. Continuous Bridges i6mo, 

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Bengough, G. D. Brass {In Press.) 

Bennett, H. G. The Manufacture of Leather 8vo, 600 

— — Animal Proteids 8vo, {In Press.) 

Bernthsen, A. A Text-book of Organic Chemistry. 12H10, 

Bersch, J. Manufacture of Mineral and Lake Pigments 8vo, 

Beveridge, J. Papermaker's Pocket Book. i2mo, 

Binnie, Sir A. Rainfall Reservoirs and Water Supply 8vo, 

Binns, C. F. Manual of Practical Potting .8vo, 

The Potter's Craft ; i2mo y 

Birchmore, W. H. Interpretation of Gas Analysis i2mo, 

Blaine, R. G. The Calculus and Its Applications. 12010, 

Blanchard, W. M. Laboratory Exercises in General Chemistry. .12010, 

Blasdale, W. C. Quantitative Chemical Analysis ». 12010, 

Bloch, L. Science of Illumination.. 8vo, 

Blyth, A. W. Foods: Their Composition and Analysis 8vo, 

■ Poisons: Their Effects and Detection ,. .8vo, 

Bockmann, F. Celluloid i2mo, 

Bodmer, G. R. Hydraulic Motors and Turbines 12010, 

Boileau, J. T. Traverse Tables 8vo, 

Bonney, G. E. The Electro-platers' Handbook 12010, 

Boone, W. T. A Complete Course of Volumetric Analysis 12010, 

Booth, N. Guide to the Ring-spinning Frame 12010, 



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D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG ' : 5 

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Booth, W. H. Water Softening and Treatment 8vo, 3 50 

Superheaters and Superheating and Their Control 8vo, *i 50 

Bottcher, A. Cranes: Their Construction, Mechanical Equipment and 

Working 4to (Reprinting.)' 

Bottler, M. Modern Bleaching Agents i2mo, 

Bottone, S. R. Magnetos for Automobilists i2mo, 

Electro-Motors, How Made and How Use i2mo, 

Boulton, S. B. Preservation of Timber i6mo, 

Bourcart, E. Insecticides, Fungicides and Weedkillers 8vo, 

Bourgougnon, A. Physical Problems i6mo, 

Bourry, E. Treatise on Ceramic Industries 8vo, 

Bowie, A. J., Jr. A Practical Treatise on Hydraulic Mining 8vo, 

Bowls, 0. Tables of Common' Rocks i6mo, 

Bowser, E. A. Elementary Treatise on Analytic Geometry i2mo, 

Elementary Treatise on the Differential and Integral Calculus . i2mo, 

Elementary Treatise on Analytic Mechanics i2mo, 

Elementary Treatise on Hydro-mechanics i2mo, 

A Treatise on Roofs and Bridges i2mo, 

Boycott, G. W. M. Compressed Air Work and Diving 8vo, 

Bradford, G. Whys and Wherefores of Navigation 121110, 2 00 

Sea Terms and Phrases i2mo, fabrikoid (In Press.) 

Bragg, E. M. Design of Marine Engines and Auxiliaries 8vo, 4 00 

Brainard, F. R. The Sextant i6mo, 

Brassey's Naval Annual for 1919 8vo, 

Briggs, R., and Wolff, A. R. Steam-Heating i6mo, 

Bright, C. The Life Story of Sir Charles Tilsoj. Bright 8vo, 

. Telegraphy, Aeronautics and War : 8vo, 

Brislee, T. J. Introduction to the Study of Fuel 8vo, 

Broadfoot, S. K. Motors: Secondary Batteries i2mo, 

Broughton, H. H. Electric Cranes and Hoists 

Brown, G. Healthy Foundations i6mo, 

Brown, H. Irrigation 8vo, 

Brown, H. Rubber 8vo, 

W. A. Portland Cement Industry 8vo, 

Brown, Wm. N. Dipping, Burnishing, Lacquering and Bronzing 

Brass Ware i2mo, 

Handbook on Japanning i2mo, 

Brown, Wm. N. The Art of Enamelling on Metal i2mo, 

House Decorating and Painting i2mo, 

History of Decorative Art i2mo 

Workshop Wrinkles 8vo, 

Browne, C. L. Fitting and Erecting of Engines 8vo, 

Browne, R. E. Water Meters i6mo, 

Bruce, E. M. Detection of Common Food Adulterants i2mo, 

Brunner, R. Manufacture of Lubricants, Shoe Polishes and Leather 

Dressings 8vo, 

Buel, R. H. Safety Valves i6mo, 

Bunkley, J. W. Military and Naval Recognition Book i6mo, 

Burley, G. W. Lathes. Their Construction and Operation i2mo, 

. Machine and Fitting Shop Practice. 2 vols i2mo, each, 

Testing of Machine Tools 121110, 

Burnside, W. Bridge Foundations i2mo, 



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6 D, VAN NOSTRAND CO.'S SHORT TITLE CATALOG 

Burstall, F. W. Energy Diagram lor Gas. With Text 8vo, i 50 

Diagram. Sold separately * x 00 

Burt, W. A. Key to the Solar Compass i6mo, leather, 250 

Buskett, E. W. Fire Assaying I2mo * x *- 

Butler, H. J. Motor Bodies and Chassis 8vo) *3 00 

Byers, H. G., and Knight, H. G. Notes on Qualitative Analysis 8vo, 

(New Edition in Preparation.) 

Cain, W. Brief Course in the Calculus ,,«/.,.<,, i2mo, *i 75 

• Elastic Arches i6mo, o 75 

Maximum Stresses i6mo, o 75 

Practical Designing Retaining of Walls i6mo, o 75 

Theory of Steel-concrete Arches and of Vaulted Structures. 

i6mo, o 75 

■ Theory of Voussoir Arches i6mo, o 75 

■ Symbolic. Algebra i6mo, 

Calvert, G. T. The Manufacture of Sulphate of Ammonia and 

Crude Ammonia i2mo, 

Camm, S.> Aeroplane Construction i2mo, 3 00 

Carnart, H. S. Tnermo Electromotive Force in Electric Cells. . .121110, 2 00 

Carey, A. E., and Oliver, F. W. Tidal Lands 8vo, 5 00 

Carpenter, F. D. Geographical Surveying i6mo, 

Carpenter, R. C, and Diederichs, H. Internal Combustion Engines. 8vo, 5 50 

uarpmaex, H. Electric Welding and Welding Appliances 4to, 5 00 

Carter, H. A. Ramie (Rhea), China Grass i2mo, *3 00 

Carter, H. R. Modern Flax, Hemp, and Jute Spinning 8vo, *3 50 

Bleaching, Dyeing and Finishing of Fabrics 8vo, *i 25 

Cary, E. R. Solution of Railroad Problems with the Slide Rule.i6mo, 1 25 

Casler, M. D. Simplified Reinforced Concrete Mathematics i2mo, 1 25 

Cathcart, W. L. Machine Design. Part I. Fastenings 8vo, *3 50 

Cathcart, W. L., and Chaffee, J. I. Elements of Graphic Statics. . .8vo, *3 00 

— -—■ Short Course in Graphics i2mo, 1 50 

Caven, R. M., and Lander, G. D. Systematic Inorganic Chemistry. i2mo, 2 25 

Chalkley, A. P. Diesel Engines 8vo, 5 00 

Chalmers. T. W. The Production and Treatment of Vegetable Oils, 

4to, 7 50 

Paper Making and its Machinery , 4to, 8 00 

The Gyroscopic Compass 8vo, 5 00 

Chambers' Mathematical Tables 8vq, 2 50 

Chambers, G. F. Astronomy i6mo 2 50 

Chappel, E. Five Figure Mathematical Tables 8vo, 250 

Charnock, Mechanical Technology 8vo, 3 50 

Charpentier, P. Timber 8vo, *6 00 

Chatley, H. Principles and Designs of Aeroplanes i6mo, o 75 

How to Use Water Power 121110, *i 5c 

Gyrostatic Balancing 8vo, *i 25 

Child, C. D. Electric Arc 8vo, *2 00 

Christian, M. Disinfection and Disinfectants i2mo, 2 50 

Christie, W. W. Boiler-waters, Scale, Corrosion, Foaming 8vo, *3 00 

— Chimney Design and Theory 8vo, *3 00 

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Church's Laboratory Guide 8vo, 2 50 



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Cisin, H. J. Modern Marine Engineering i2mo {In Press.) 

Claphara, J. H. Woolen and Worsted Industries 8vo, a oo 

Clapperton, G. Practical Papermaking. 8vo {Reprinting.) 

Clark, A. G. Motor Car Engineering. 

Vol. I. Construction * *4 oo 

Vol.11. Design 8vo, *3 50 

Clark, C. H. Marine Gas Engines. New Edition 2 00 

Clarke, J. W., and Scott, W. Plumbing Practice. 

Vol. I. Lead Working and Plumbers' Materials/". 8vo, *.. 00 

Vol. II. Sanitary Plumbing and Fittings {In Press.) 

Vol. III. Practical Lead Working on Roofs {In Press.) 

Clarkson, R. P. Elementary Electrical Engineering i2mo, 

Clerk, D., and Idell, F. E. Theory of the Gas Engine i6mo, 

Clevenger, S. R. Treatise on the Method of Government Surveying. 

i6mo, morocco, 

Clouth, F. Rubber, Gutta-Percha, and Balata 8vo, 

Cochran, J. Concrete and Reinforced Concrete Specifications 8vo, 

Treatise on Cement Specifications 8vo, 

Cocking, W. C. Calculations for Steel-Frame Structures i2mo, 

Coffin, J. H. C. Navigation and Nautical Astronomy i2mo, 

colburn, Z., and Thurston, R. H. Steam Boiler Explosions. .. .i6mo, 

Cole, R. S. Treatise on Photographic Optics 12D10, 

Coles-Finch, W. Water, Its Origin and Use 8vo, 

Collins, C. D. Drafting Room Methods, Standards and Forms 8vo, 

Collins, S. Hoare. Plant Products and Chemical Fertilizers 8vo, 

Chemical Fertilizers 8vo, 

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Switchgear i2mo, 

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Comstock, D. F., and Troland, L. T. The Nature of Electricity and 

Matter 8vo, 

Coombs, H. A. Gear Teeth i6mo, 

Cooper, W. R. Primary Batteries 8vo, 

Copperthwaite, W. C. Tunnel Shields 4to, 

Corfield, W. H. Dwelling Houses i6mo, 

Water and Water-Supply i6mo, 

Cornwall, H. B. Manual of Blow-pipe Analysis 8vo. 

Couch, J. F. Dictionary of Chemical Terms i2mo, fabrikoid, 

Cowee, G. A. Practical Safety Methods and Devices 8vo, 

Cowell, W. B. Pure Air, Ozone, and Water i2mo, 

Craig, J. W., and Woodward, W. P. Questions and Answers About 

Electrical Apparatus i2mo, leather, 

Craiff. T. Motion of a Solid in a Fuel i6mo, 

Wave and Vortex Motion i6mo, 

Crehore, A. C. Mystery of Matter and Energy 8vo, 

The Atom i2mo, 

Crocker, F. B., and Arendt, M. Electric Motors 8vo, 

Crocker, F. B., and Wheeler, S. S. The Management of Electrical Ma- 
chinery .*.... i2mo, *i 00 

Crosby, E. U., Fiske, H. A., and Forster, H. W. Handbook of Fire 

Protection i2mo, 400 

Cross, C. F., Bevan, E. J., and Sindall, R. W. Wood Pulp and Its 

Uses 8vo, 3 50 

Crosskey, L. R. Elementary Perspective 8vo, 1 50 



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8 D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG 

Crosskey, L. R., and Thaw, J. Advanced Perspective. 8vo, 2 06 

Culley, J. L. Theory of Arches i6mo, o 75 

Cushing, H. C., Jr., and Harrison, N. Central Station Management. .. *2 00 

Dadourian, H. M. Analytical Mechanics i2mo, 

Graphic Statics . 8vo, 

Danby, A. Natural Rock Asphalts and Bitumens 8vo, 

Darling, E. R. Inorganic Chemical Synonyms i2mo, 

Davenport, C. The Book 8vo, 

Davey, N. The Gas Turbine 8vo, 

Davies, F. H. Electric Power and Traction 8vo, 

Davis, A. M. Introduction to Palaeontology 8vo, 

— — Foundations and Machinery Fixing i6mo, 

Deerr, N. Sugar Cane 8vo (Reprinting.) 

Deite, C. Manual of Toilet Soap-Making 8vo, 

De la Coux, H. The Industrial Uses of Water 8vo, 

Del Mar, W. A. Electric Power Conductors 8vo, *2 00 

Denny, G. A. Deep-level Mines of the Rand 4to, *io 00 

De Roos, J. D. C. Linkages i6mo, o 75 

Derr, W. L. Block Signal Operation Oblong i2mo, 

Desaint, A. Three Hundred Shades and How to Mix Them 8vo, 

De Varona^ A. Sewer Gases i6mo, 

Devey, R. G. Mill and Factory Wiring i2mo, 

Dichmann, Carl. Basic Open- Hearth Steel Process. i2mo, 

Dieterich, K. Analysis of Resins, Balsams, and Gum Resins. .. .8vo, 

Dilworth, E. C. Steel Railway Bridges 4to, 

Dinger, Lieut. H. C. Care and Operation of Naval Machinery. . ,i2mo, 
Dixon, D. B. Machinist's and Steam Engineer's Practical Calculator. 

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Dorr, B. F. The Surveyor's Guide and Pocket Table-book. 

i6mo, morocco, 
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Draper, E. G. Navigating the Ship i2mo, 

Dubbel, H. High Power Gas Engines 8vo, 

Dumesny, P., and Noyer, J. Wood Products, Distillates, and Extracts. 

8vo, 
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8vo, 
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Dunstan, A. E., and Thole, F. B. T. Textbook of Practical Chemistry. 

i2mo, 

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Duthie, A. L. Decorative Glass Processes 8vo, 

Dwight, H. B. Transmission Line Formulas 8vo, 

Dyke, A. L. Dyke's Automobile and Gasoline Engine Encyclopedia, 

8vo, 

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Dyson, S. S., and Clarkson, S. S. Chemical Works 8vo, 

Eccles, W. H. Wireless Telegraphy and Telephony • i2mo, 



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D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG 

Eck, J. Light, Radiation and Illumination 8vo, 

Eddy, L. C. Laboratory Manual of Alternating Currents i2mo, 

Edelman, P. Inventions and Patents i2mo, 

Edgcumbe, K. Industrial Electrical Measuring Instruments 8vo, 

Edler, R. Switches and Switchgear ; 8vo, 

Eissler, M. The Metallurgy of Gold 8vo, 

The Metallurgy of Silver 8vo, 

The Metallurgy of Argentiferous Lead 8vo, 

A Handbook on Modern Explosives 8vo, 

Ekin, T. C. Water Pipe and Sewage Discharge Diagrams folio, 

Electric Light Carbons, Manufacture of 8vo, 

Eliot, C. W., and Storer, F. H. Compendious Manual of Qualitative 

Chemical Analysis i2mo, 

Eliott, A. W. M. Rectangular Areas. i2mo, 

Ellis, C. Hydrogenation of Oils 8vo, 

Ultraviolet Light, Its Applications in Chemical Arts i2mo, 

(In Press) 

and Meigs, J. V. Gasolene and Other Motor Fuels.. (In Press.) 

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Applied Thermodynamics 8vo, 

Vapors for Heat Engines '. i2mo, 

Ermen, W. F. A. Materials Used in Sizing 8vo, 

Erwin, M. The Universe and the Atom i2mo (Reprinting.) 

Ewing, A. J. Magnetic Induction in Iron 8vo, 500 

Fage, A. Airscrews in Theory and Practice 4to, 

Fairchild, J. F. Graphical Compass Conversion Chart and Tables. . . 

Fairie, J. Notes on Lead Ores i2mo, 

Notes on Pottery Clays i2mo, 

Fairley, W., and Andre, Geo. J. Ventilation of Coal Mines. .. .i6mo, 

Fairweather, W. C. Foreign and Colonial Patent Laws 8vo, 

Falk, K. G. Chemical Reactions: Their Supply and Mechanism. .i2mo, 

Fanning, J. T. Hydraulic and Water-supply Engineering 8vo, 

Farnsworth, P. V. Shop Mathematics nmo (In Press.) 

Fay, I. W. The Coal-tar Dyes 8vo, 

Fernbach, R. L. Glue and Gelatine 8vo, 

Findlay, A. The Treasures of Coal Tar nmo, 

Firth, J. B. Practical Physical Chemistry i2mo, 

F'r.cher, E. The Preparation of Organic Compounds i2mo, 

Fisher, H. K. C, and Darby, W. C. Submarine Cable Testing. . .8vo, 

Fleischmann, W. The Book of the Dairy 8vo, 

Fleming, J. A, The Alternate-current Transformer. Two Volumes. 8vo. 

Vol. I. The Induction of Electric Currents '. *6 50 

Vol, II. The Utilization of Induced Currents 

Propagation of Electric Currents 8vo, 

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Volumes 8vo, each, 

Fleury, P. Preparation and Uses of White Zinc Paints 8vo, 

Flynn, P. J. Flow of Water i2mo, 

Hydraulic Tables i6mo, 



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IO D. WN NOSTRAND CO.'S SHORT TITLE CATALOG 

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Fowle, F. F. Overhead Transmission Line Crossings i2mo, *i 5© 

The Solution of Alternating Current Problems Svo {In Press.) 

Fox, W. G. Transition Curves i6mo, o 75 

Fox, W., and Thomas, C. W. Practical Course in Mechanical Draw- 
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Foye, J. C. Chemical Problems i6mo, o 75 

t Handbook of Mineralogy i6mo, o 75 

Francis, J. B. Lowell Hydraulic Experiments 4to, 15 00 

Franzen, H. Exercises in Gas Analysis i2mo, *i 00 

Fraser, E. S., and Jones, R. B. Motor Vehicles and Their Motors, 

Svo, fabrikoid, 2 00 

Freudemacher, P. W< Electric Mining Installations i2mo, 1 00 

Friend, J. N. The Chemistry of Linseed Oil iamo, 1 00 

Fritsch, J. Manufacture of Chemical Manures 8vo, 5 00 

Frye, A. I. Civil Engineers' Pocket-book nmo, leather, *5 00 

Fuller, G. W. Investigations into the Purification of the Ohio River. 

4to, *io 00 

Furaell, J. Paints, Colors, Oils, and Varnishes 8vo. 

Gant, L. W. Elements of Electric Traction 8vo, *2 50 

Garcia, A. J. R. V. Spanish-English Railway Terms 8vo, 3 00 

Gardner, H. A. Paint Researches, and Their Practical Applications, 

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Fires i2mo, leather, * 1 50 

Garrard, C. C. Electric Switch and Controlling Gear 8vo, *6 00 

Gaudard, J. Foundations i6mo, o 75 

Gear, H. B., and Williams, P. F. Electric Central Station Distribution 

Systems 8vo, *3 50 

Geerligs, H. Cw P. Cane Sugar and Its Manufacture 8vo, *6 00 

— — Chemical Control in Cane Sugar Factories... 4to, 500 

Geikie, J. Structural and Field Geology Svo, 750 

Mountains. Their Growth, Origin and Decay 8vo, 4 50 

The Antiquity of Man in Europe 8vo, *3 00 

Georgi, F., and Schubert, A. Sheet Metal Working -8vo, 350 

Gerhard, W. P. Sanitation, Watersupply and Sewage Disposal of Country 

Houses i2mo, 2 50 

Gas Lighting i6mo, o 75 

Household Wastes i6mo, o 75 

House Drainage . i6mo, o 75 

■ Sanitary Drainage of Buildings i6mo, o 75 

Gerhardi, C. W. H. Electricity Meters 8vo, *j 20 

Geschwind, L. Manufacture of Alum and Sulphates 8vo, 5 00 

Gibbings, A. H. Oil Fuel Equipment for Locomotives. 8vo. 

{Reprinting.) 

Gibbs, W. E. Lighting by Acetylene i2mo, *i 50 

Gibson, A. H. Hydraulics and Its Application 8vo, 6 00 

■ Water Hammer in Hydraulic Pipe Lines i2mo, 2 50 

Gibson, A. H., and Ritchie, E. G. Circular Arc Bow Girder 4to, *3 50 



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D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG jr 

Gilbreth, F. B. Motion Study "mo, ■ 

Primer of Scientific Management i2mo, 

Gill A. H. Gas Analysis for Chemists 8vo, 

Gillinore, Gen. Q. A. Roads, Streets, and Pavements i2mo, 

Godfrey, E. Tables for Structural Engineers i6mo, leather, 

Golding, H. A. The Theta-Phi Diagram iamo, 

Goldschmidt, R. Alternating Current Commutator Motor 8vo, 

Goodchild, W. Precious Stones 8vo, 

Goodell, J. M. The Location, Construction and Maintenance of 

Roads 8v0 » 

Goodeve, T. M. Textbook on the Steam-engine i2mo, 

Gore, G. Electrolytic Separation of Metals 8vo, 

Gould, E. S. Arithmetic of the Steam-engine T2mo, 

Calculus i6mo, 

High Masonry Dams i6mo, 

Gould, E. S. Practical Hydrostatics and Hydrostatic Formulas. .i6mo, 

Goulding, E. Cotton and Other Vegetable Fibres 8vo, 

Gratacap, L. P. A Popular Guide to Minerals 8vo, 

Gray, H. H. Gas-Works Products 8vo (In Press.) 

Gray, J. Electrical Influence Machines nmo, 

Marine Boiler Design i2mo (Reprinting.) 

Greenhill, G. Dynamics of Mechanical Flight 8vo, 

Greenwood, H. C. The Industrial Gases 8vo, 

Gregorius, R. Mineral Waxes i2mo, 

Grierson, R. Some Modern Methods of Ventilation 8vo, 

Griffiths, A. B. A Treatise on Manures 121110 (Reprinting.) 

Gross, E. Hops 8vo, 

Grossman, J. Ammonia and Its Compounds 121110, 

Groth, L. A. Welding and Cutting Metals by Gases or Electricity. 

8vo, 

Grover, F. Modern Gas and Oil Engines \ 8vo, 

Gruner ? A. Power -loom Weaving 8vo, 

Gnmsky, C. E. Topographic Stadia Surveying i6mo, 

Gunther, C. 0. Integration 8vo, 

Gurden, R. L. Traverse Tables folio, 

Guy, A. E. Experiments on the Flexure of Beams 8vo, 

Haenig, A. Emery and Emery Industry. 8vo, 

Hainbach, R. Pottery Decoration i2mo, 

Hale, A. J. The Manufacture of Chemicals by Electrolysis 8vo, 

Hale, Harrison. American Chemistry i2mo (In Press.) 

Hale, W. J. Calculations of General Chemistry i2mo, 

Hall, C. H. Chemistry of Paints and Paint Vehicles 121110, 

Hall, R. H. Governors and Governing Mechanism i2mo, 

Hall, W. S. Elements of th* Differential and Integral Calculus. .. .8vo, 
Descriptive Geometry 8vo volume and a 4to atlas, 

Haller, G. F., and Cunningham, E. T. The Tesla Coil i2mo, 

Halsey, F. A. Slide Valve Gears i2mo, 

The Use of the Slide Rules i6mo, 

Worm and Spiral Gearing i6mo, 

Hamlin, M. L. Action of Chemicals on Industrial Materials. .Svo, 

(In Press.) 



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12 D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG 

Hancock, H. Textbook of Mechanics and Hydrostatics 8vo, i 50 

Hardy, E. Elementary Principles of Graphic Statics i2mo, *i 50 

Haring, H. Engineering Law. 

Vol. I. Law of Contract 8vo, *4 00 

Harper, J. H. Hydraulic Tables, on the Flow of Water i6mo, *2 00 

Harris, S. M. Practical Topographical Surveying (In Press.) 

Harrow, B. Eminent Chemists of Our Times: Their Lives and Work. 2 50 

v 

■ From Newton to Einstein 121110, 1 00 

Harvey, A. Practical Leather Chemistry 8vo, 6 00 

Haskins, C. H. The Galvanometer and Its Uses : i6mo, 1 50 

Hatt, J. A. H. The Colorist square i2mo, * 2 00 

Hausbrand, E. Drying by Means of Air and Steam i2mo, 2 50 

Evaporating, Condensing and Cooling Apparatus 8vo, 6 00 

Hausmann, E. Telegraph Engineering ;8vo, *3 00 

Hausner, A. Manufacture of Preserved Foods and Sweetmeats 8vo, 3 50 

Hawkesworth, J. Graphical Handbook for Reinforced Concrete Design. 

4to, 2 00 

Hay, A. Continuous Current Engineering 8vo, 3 75 

Hayes, H. V. Public Utilities, Their Cost New and Depreciation. . .8vo, *2 00 

Public Utilities, Their Fair Present Value and Return. 8vo, *2 00 

Heath, F. H. Chemistry of Photography 8vo. (In Press.) 

Heather, H. J. S. Electrical Engineering.. 8vo, 450 

Heaviside, 0. Electromagnetic Theory. Vols. I and II....8vo, each, 

(Reprinting.) 

Vol. Ill 8vo (Reprinting.)- 

Heck, R. C. H. The Steam Engine and the Turbine .8vo, 4 50 

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Vol. I. Thermodynamics and the Mechanics 8vo, 

Vol. II. Form, Construction, and Working 8vo, 

Notes on Elementary Kinematics 8vo, boards, 

Graphics of Machine Forces 8vo, boards, 

Heermann, P. Dyers' Materials i2mo, 

Hellot, Macquer and D'Apligny. Art of Dyeing Wool, Silk and Cotton. 8vo, 
Hering, C, and Getman, F. H. Standard Tables of Electro-Chemical 

Equivalents 121110, 

Hering, D. W. Essentials of Physics for College Students. ..*.. .8vo, 

Herington, C. F. Powdered Coal as Fuel 8vo, 

Herrmann, G. The Graphical Statics of Mechanism 121110, 

Herzfeld, J. Testing of Yarns and Textile Fabrics 8vo. 



Hildenbrand, B. W. Cable-Making i6mo, 

Hilditch, T. P. A Concise History of Chemistry 121110, 

Hill, M. J. M. The Theory of Proportion 8vo, 

Hillhouse, P. A. Ship Stability and Trim 8vo, 

Hiroi, I. Plate Girder Construction i6mo, 

/Statically-Indeterminate Stresses 121110, 

Hirshfeld, C. F. Engineering Thermodynamics. i6mo, 

Hoar, A. The Submarine Torpedo Boat 121110. 

Hobart, H. M. Heavy Electrical Engineering 8vo, 

— — Design of Static Transformers 121110, 

Electricity 8vo, 

Electric Trains 8vo (Reprinting.) 

Electric Propulsion of Ships 8vo, *2 50 



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D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG 13 

Hobart, J. F. Hard Soldering, Soft Soldering and Brazing i2mo, 1 25 

Hobbs, W. R. P. The Arithmetic of Electrical Measurements. .. .i2mo, o 75 

Hoff, J. N. Paint and Varnish Facts and Formulas i2mo, 2 00 

Hole, W. The Distribution of Gas 8vo, *8 50 

Holmes, A. Nomenclature of Petrology 8vo, 5 00 

Hopkins, N. M. Model Engines and Small Boats i2mo, 1 25 

The Outlook for Research and Invention i2mo. 2 00 

Eopkinson, J., Shoolbred, J. N., and Day, R. E. Dynamic Electricity. 

i6mo. o 75 

Horner, J. Practical Ironfounding 8vo, *2 00 

Gear Cutting, in Theory and Practice 8vo (Reprinting.) 

Houghton, C. E. The Elements of Mechanics of Materials i2mo, 

Houstoun, R. A. Studies in Light Production i2mo, 

Hovenden, F. Practical Mathematics for Young Engineers i2mo, 

Howe, G. Mathematics for the Practical Man '. i2mo, 

Eoworth, J. Repairing and Riveting Glass, China and Earthenware. 

8vo, paper, 

Hoyt, W. E. Chemistry by Experimentation • 8vo, 

Hubbard, E. The Utilization of Wood-waste 8vo, 

Hiibner, J. Bleaching and Dyeing of Vegetable and Fibrous Materials. 

8vo, 

Hudson, 0. F. Iron and Steel 8vo, 

Humphreys, A. C. The Business Features of Engineering Practice . 8vo, 

Hunter, A. Bridge Work 8vo. (In Press.) 

Hurst, G. H. Handbook of the Theory of Color 8vo, 

Dictionary of Chemicals and Raw Products 8vo, 

Lubricating Oils, Fats and Greases 8vo, 

Soaps 8vo, 

Hurst, G. H., and Simmons, W. H. Textile Soaps and Oils 8vo, 

Hurst, H. E., and Lattey, R. T. Text-book of Physics 8vo, 

Also published in three parts. 

Part I. Dynamics and Heat 

Part II. Sound and Light 

Part III. Magnetism and Electricity 

Hutchinson, R. W., Jr. Long Distance Electric Power Transmission. 

i2mo, 3 00 

Hutchinson, R. W., Jr., and Thomas, W. A. Electricity in Mining. i2mo. 

(In Press.) 

Hyde, E. W. Skew Arches i6mo. 

Eyde, F. S. Solvents, Oils, Gums, Waxes 8vo, 



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Induction Coils . ..'. i6mo. 

Ingham, A. E. Gearing. A practical treatise 8vo, 

Ingle, H. Manual of Agricultural Chemistry 8vo, 

Inness, C. H. Problems in Machine Design i2mo, 

Centrifugal Pumps nmo, *3 00 

The Fan i2mo, *4 00 

Jacob, A., and Gould, E. S. On the Designing and Construction of 

Storage Reservoirs • i6mo. o 75 



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James, F. D. Controllers for Electric Motors 8vo. <* oo 

Jehl, F. Manufacture of Carbons 8vo. 5 oo 

Jennings, A. S. Commercial Paints and Painting 8vo. 2 so 

Jennison, F. H. The Manufacture of Lake Pigments 8vo, 6 00 

Jepson, G. Cams and the Principles of their Construction 8vo, *i 50 

Mechanical Drawing 8vo (In Preparation.) 

Jervis-Smith, F. J. Dynamometers 8vo. 4 00 

Jockin, W~ Arithmetic of the Gold and Silversmith i2mo, *i 00 

Johnson, C. H., and Earle, R. P. Practical Tests for the Electrical 

Laboratory ( In Press.) 

Johnson, J. H. Arc Lamps and Accessory Apparatus i2mo, o 75 

Johnson, T. M. Ship Wiring and Fitting i2mo (Reprinting.) 

Johnston, J. F. W., and Cameron, C. Elements of Agricultural Chemistry 

and Geology i2mo, 2 60 

Joly, J. Radioactivity and Geology i2mo (Reprinting.) 

Jones, H. C. Electrical Nature of Matter and Radioactivity. .. .i2mo, 

Nature of Solution 8vo, 

— — New Era in Chemistry i2mo, 

Jones, J. H. Tinplate Industry 8vo 

Jones, M. W. Testing Raw Materials Used in Paint i2mo, 

Jordan, L. C. Practical Railway Spiral i2mo, leather, 

Jiiptner, H. F. V. Siderclogy: The Science of Iron 8vo, 

Kapp, G. Alternate Current Machinery .,»»,. i6mo, 

Kapper, F. Overhead Transmission Lines 4to, 

Keim, A, W. Prevention of Dampness in Buildings 8vo, 

Keller, S. S., and Knox, W. E. Analytical Geometry and Calculus... 
Kemble, W. T., and Underhill, C. R. The Periodic Law and the Hydrogen 

Spectrum 8vo, paper, 

Kemp, J. F. Handbook of Rocks 8vo, 

Kennedy, A. B. W., and Thurston, R. H. Kinematics of Machinery. 

i6mo, 
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i6mo, 

Kennedy, R. Flying Machines ; Practice and Design i2mo, 

Principles of Aeroplane Construction 8vo, 

Kent, W. Strength of Materials i6mo, 

Kershaw, J. B. C. Fuel, Water and Gas Analysis 8vo, 

Electrometallurgy 8vo, 

Electro-Thermal Methods of Iron and Steel Production 8vo, 

The Use of Low Grade and Waste Fuel for Power Generation . 8vo, 

Kingzett, C. T. Popular Chemical Dictionary 8vo, 

Kinzbrunner, C. Continuous Current Armatures ,8vo, 

Testing of Alternating Current Machines 8vo, 

Kinzer, H., and Walter, K. Theory and Practice of Damask Weaving, 

8vo, 4 00 
Kirkaldy, A.. W., and Evans, A. D. History and Economics of 

Transport 8vo, *3 00 

1 bride, J. Engraving for Illustration 8vo, *i 00 



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D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG 15 

Kirschke, A. Gas and Oil Engines i2mo, *i 50 

Klein, J. F. Design of a High-speed Steam-engine 8vo, *5 00 

Physical Significance of Entropy 8vo, *i 50 

Klingenberg, G. Large Electric Power Stations 4to, 9 00 

Knight, R.-Adm. A. M. Modern Seamanship. . : 8vo, *6 50 

Pocket Edition i2mo, f abrikoid, 3 00 

Knott, C. G., and Mackay, J. S. Practical Mathematics 8vo, 2 50 

Knox, J. Physico-Chemical Calculations i2mo, 1 50 

Fixation of Atmospheric Nitrogen 121110, 1 00 

Koester, F. Steam-Electric Power Plants 4to, *5 00 

Hydroelectric Developments and Engineering 4to, 600 

Koller, T. The Utilization of Waste Products., 8vo, *5 00 

Cosmetics 8vo, 3 50 

Koppe, S. W. Glycerine i2mo, *3 50 

Kozmin, P. A. Flour Milling 8vo, 8 50 

Krauch, C. Chemical Reagents 8vo, 7 00 

Kremann, R. Application of the Physico-Chemical Theory to Tech- 
nical Process and Manufacturing Methods 8vo, 3 00 

Kretchmar, K. Yarn and Warp Sizing 8vo, *5 00 

Laff argue, A. Attack in Trench Warfare i6mo, o 50 

Lallier, E. V. Elementary Manual of the Steam Engine i2mo, *2 00 

Lambert, T. Lead and Its Compounds 8vo, *3 50 

— — Bone Products and Manures 8vo, *3 50 

Lamborn, L. L. Cottonseed Products 8vo, 4 00 

Modern Soaps, Candles, and Glycerin 8vo, 1000 

Lamprecht, R. Recovery Work After Pit Fires 8vo, 5 00 

Lanchester, F. W. Aerial Flight. Two Volumes. 8vo. 

Vol. I. Aerodynamics *6 00 

Vol. II. Aerodonetics *6 00 

Lanchester, F. W. The Flying Machine 8vo, 

Industrial Engineering: Present and Post-War Outlook. . .121110, 

Lange, K. R. By-Products of Coal-Gas Manufacture i2mo, 

La Rue, B. F. Swing Bridges i6mo, 

Lassar-Cohn, Dr. Modern Scientific Chemistry 121110, 

Latimer, L. H., Field, C. J., and Howell, J. W. Incandescent Electric 

Lighting i6mo, 

Latta, M. N. Handbook of American Gas-Engineering Practice. .8vo, 

American Producer Gas Practice 4to, 

Laws, B. C. Stability and Equilibrium of Floating Bodies 8vo, 

Lawson, W. R. British Railways. A Financial and Commercial 

Survey 8vo, 

Leask, A. R. Refrigerating Machinery 121110 (Reprinting.) 

Lecky, S. T. S. "Wrinkles" in Practical Navigation 8vo, 

Pocket Edition 121110, 

Danger Angle i6mo, 

Le Doux, M. Ice-Making Machines i6mo, 

Leeds, C. C. Mechanical Drawing for Trade Schools oblong 4to, 

Mechanical Drawing for High and Vocational Schools 4to, 

Principles of Engineering Drawing 8vo, 

Lefevre, L. Architectural Pottery 4to, 

Lehner, S. Ink Manufacture 8vo, 

Lemstrom, S. Electricity in Agriculture and Horticulture 8vo, 

Letts, E. A. Fundamental Problems in Chemistry ...*. .8vo, *2 00 



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16 D. VAN NOSTRAND CO.'S SHORT ^ITLE CATALOG 

Le Van, W. B. Steam-Engine Indicator i6mo, o 75 

Lewes, V.'B. Liquid and Gaseous Fuels .8vo, 3 00 

Carbonization of Coal 8vo, *5 00 

Lewis Automatic Machine Rifle ; Operation of i6mo, *o 60 

Licks, H. E. Recreations in Mathematics 121110, 1 50 

Lieber, B; F. Lieber's Five Letter American Telegraphic Code .8vo, *is 00 

Spanish Edition 8vo, *i5 00 

French Edition 8vo, *i5 00 

Terminal Index 8vo, *2 50 

Lieber's Appendix , folio, *I5 00 

Handy Tables 4to, *2 50 

Bankers and Stockbrokers' Code and Merchants and Shippers' 

Blank Tables 8vo, *is 00 

100,000,000 Combination Code 8vo, *io 00 

Livermore, V. P., and Williams, J. How to Become a Competent Motor- 
man nmo, *i 00 

Livingstone, R. Design and Construction of Commutators 8vo, 4 50 

Mechanical Design and Construction of Generators 8vo, 4 50 

Lloyd, S. L. Fertilizer Materials 121110, 2 00 

Lockwood, T. D. Electricity- Magnetism, and Electro-telegraph .. .8vo, 250 

— Electrical Measurement and the Galvanometer i2mo, o 75 

Lodge, O. J. Elementary Mechanics . i2mo, 1 50 

Loewenstein, L. C, and Crissey, C. P. Centrifugal Pumps 5 00 

Lomax, J. W. Cotton Spinning i2mo, 1 50 

Lord, R. T. Decorative and Fancy Fabrics 8vo, *3 50 

Loring, A. E. A Handbook of the Electromagnetic Telegraph. ..i6mo, o 75 

Lowy, A. Organic Type Formulas o 10 

Lubschez, B. J. Perspective i2mo, 2 00 

Lucke, C. E. Gas Engine Design 8vo, *3 00 

Power Plants: Design, Efficiency, and Power Costs. 2 vols. 

(In Preparation.) 

Luckiesh, M. Color and Its Application 8vo, 3 50 

Light and Shade and Their Applications 8vo, 3 00 

Visual Illusions (In Preparation.) 

Lunge, G. Coal-tar and Ammonia. Three Volumes 8vo, *2$ 00 

Technical Gas Analysis 8vo, *4 50 

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Vol. I. Supplement 8vo (Reprinting.) 

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parts , (In Press.) 

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Technical Chemists' Handbook i2mo, leather, *4 00 

Technical Methods of Chemical Analysis. 

Vol. I. In two parts 8vo (New Edition in Press.) 

Vol. II. In two parts 8vo (New Edition in Press.) 

Vol. III. In two parts 8vo (New Edition in Press.) 

The set (3 vols.) complete 



D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG 17 

Luquer, L. M. Minerals in Rock Sections. 8vo, 1 75 

MacBride, J. D. A Handbook of Practical Shipbuilding, 

i2mo, fabrikoid, 2 00 

Macewen, H. A. Food Inspection 8vo, *2 50 

Mackenzie, N. F. Notes on Irrigation Works 8vo, *2 50 

Mackie, J. How to Make a Woolen Mill Pay 8vo, *2 00 

Maguire, Wm. R. Domestic Sanitary Drainage and Plumbing . . . .8vo, 4 00 

Malcolm, H. W. Submarine Telegraph Cable 9 00 

Malinovzsky, A. Analysis of Ceramic Materials and Methods of 

Calculation (In Press.) 

Mallet, A. Compound Engines. i6mo, 

Mansfield, A. N. Electro-magnets i6mo, o 75 

Marks, E. C. R. Construction of Cranes and Lifting Machinery. i2mo, *2 75 

Manufacture of Iron and Steel Tubes i2mo, 2 50 

Mechanical Engineering Materials i2mo, *i 50 

Marks, G. C. Hydraulic Power Engineering 8vo, 4 50 

Marlow, T. G. Drying Machinery and Practice .... 8vo (Reprinting.) 

Marsh, C. F. Concise Treatise on Reinforced Concrete 8vo, *2 50 

■ Reinforced Concrete Compression Member Diagram. Mounted on 

Cloth Boards *i . 50 

Marsh, C. F., and Dunn, W. Manual of Reinforced Concrete and Con- 
crete Block Construction i6mo, 2 00 

Marshall, W. J., and Sankey, H. R. Gas Engines 8vo, 2 00 

Martin, G. Triumphs and Wonders of Modern Chemistry 8vo, *3 00 

Modern Chemistry and Its Wonders 8vo, *3 00 

Martin, N. Properties and Design of Reinforced Concrete 8vo, 1 50 

Martin, W. D. Hints to Engineers i2mo, 2 00 

Massie, W. W., and Underhill, C. R. Wireless Telegraphy and Telephony. 

i2mo, *i 00 

Mathot, R. E. Internal Combustion Engines 8vo, 5 00 

Maurice, W. Electric Blasting Apparatus and Explosives 8vo, *3 50 

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Maxwell, F. Sulphitation in White Sugar Manufacture i2mo, 400 

Maxwell, J. C. Matter and Motion i6mo, o 75 

Maxwell, W. H., and Brown, J. T. Encyclopedia of Muni ipal and Sani- 
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Mayer, A. M. Lecture Notes on Physics 8vo, 2 00 

McCracken, E. M., and Sampson, C. H. Course in Pattern Making. 

(In Press.) 

McCullough, E. Practical Surveying i2mo, 3 00 

McCullough, R. S. Mechanical Theory of Heat 8vo, 3 50 

McGibbon. W. C. Indicator D^ajrams for Marine Engineers 8vo, *3 50 

Marine Engineers' Drawine Book oblong 5 4to, *2 50 

McGibbon, W. C. Marine Engineers Pocketbook i2mo, *4 50 

Mcintosh, J. G. Technology of Sugar 8vo, *6 00 

Industrial Alcohol 8vo, *3 50 

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8vo. 

Vol. I. Oil Crushing, Refining and Boiling 7 00 

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18 D VAN frOSTRAND CO.'S SHORT TITLE CATALOG 

WcKillop. M., and McKillop, A. D. Efficiency Methods i2mo, 

McKnight J. D„ and Brown, A. W. Marine Multitubular Boilers 

McMaster J B. Bridge and Tunnel Centres i6mo, 

McMe-hen, F. L. Tests for Ores, Mineral? and Metals 121110, 

McNair, F. V Handbook IV Naval Gfficers i2mo, 

Meade, A. Modern Gae Works Practice 8vc, 

Melick, C. W- Tairv Laboratory Guide . . . nmo, 

M Mentor." Self -Instruction for Students in Gas Supply. i2mo. 

Elementary 

Advanced ... ... 

Self-Instruction for Students in Gas Engineering. i2mo. 

Elementary 

Advanced , 

Merivale, J. H. Notes and Formulae for Mining Students i2mo, 

Merritt, Wm. H. Field Testing for Gold and Silver i6mo, leather, 

Mertens. Tactics and Technique of River Crossings 8vo, 

Mierzinski, S. Waterproofing of Fabrics 8vo, 

Miessner, B. F. Radio Dynamics i2mo, 

Miller, G. A. Determinants i6mo, 

Miller, W. J Introduction to Historical Geology i2mo, 

Milroy, M. E. W. Home Lace-making i2mo, 

Church Lace i2mo, 

Mills, C. N Elementary Mechanics for Engineers 8vo, 

Mitchell, C. A. Mineral and Aerated Waters 8vo, 

Mitchell, C A., and Prideaux, R. M. Fibres Used in Textile and Allied 

Industries 8vo, 3 50 

Mitchell, C. F., and G. A. Building Construction and Drawing. i2mo. 

Elementary Course ... 2 50 

Advanced Course 4 50 

Monckto^ C. C. F, Radiotelegraphy 8vo, 200 

Monteverde, R. D. Vest Pocket Glossary of English-Spanish, Spanish- 
English Technical Terms 64mo, leather, 

Montgox ./y, J. H. Electric Wiring Specifications i6mo, 

Moore, E. C. S New Tables for the Complete Solution of Ganguillet and 

Kutter's Formula 8vo, 

Moore, Harold. Liquid Fuel for Internal Combustion Engines. . .8vo, 
Morecroft, J. H., and Hehre, F. W. Short Course in Electrical Testing. 

8vo, 
Morgan, A. P Wireless Telegraph Construction for Amateurs. .i2mo, 

Morgan, J. D Principles of Electric Spark Ignition 8vo, 

Morrell, R S., and Waele, A. E. Rubber, Resins, Paints and Var- 
nishes ' 8vo (In Press.) 

Moses, A. J The Characters of Crystals 8vo, 

and Parsons, C. L. Elements of Mineralogy 8vo, 

Moss, S. A. Elements of Gas Engine Design i6mo, 

The Lay-out of Corliss Valve Gears i6mo, 

Mulford, A. C. Boundaries and Landmarks . i2mo, 

Munby, A. E. Chemistry and Physics of Building Materials. .. .8vo, 

Murphy, J G. Practical Mining i6mo, 

Murray, B. M. Chemical Reagents 8vo, 

Murray, J. A. Soils and Manures ,,,,,,,,,,,, 8vo, 

Nasmith, J. The Student's Cotton Spinning 8vo, 4 50 

Recent Cotton Mill Construction i2mo, 3 00 



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D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG 19 

Neave, G. B., and Heilbron, I. M. Identification of Organic Compounds. 

i2mo, 1 50 

Neilson, R. M. Aeroplane Patents , 8vo, *2 00 

Nerz, F. Searchlights 8vo (Reprinting.) 

Newbigin, M. I., and Flett, J. S. James Geikie, the Man and the 

Geologist 8vo, 3 50 

Newbiging, T. Handbook for Gas Engineers and Managers 8vo, 7 50 

Newell, F. H., and Drayer, C. E. Engineering as a Career. .i2mo, cloth, *i 00 

Nicol, G. Ship Construction and Calculations 8vo, *io 00 

Nipher, F. E. Theory of Magnetic Measurements i2mo, 1 00 

Nisbet, H. Grammar of Textile Design 8vo, 7 50 

Nolan, H. The Telescope i6mo, o 75 

Norie, J. W. Epitome of Navigation (2 Vols.) octavo, 15 00 

A Complete Set of Nautical Tables with Explanations of Their 

Use . , octavo, 6 50 

North, H. B. Laboratory Experiments in General Chemistry i2mo, *i 00 

O'Connor, H. The Gas Engineer's Pocketbook i2mo, leather, 5 00 

Ohm, G. S., and Lockwood, T. D. Galvanic Circuit i6mo, o 75 

Olsen, J. C. Text-book of Quantitative Chemical Analysis 8vo, 4 00 

Orrasby, M. T. M. Surveying i2mo, 2 00 



Pakes, W. C. C, and Nankivell, A. T. The Science of Hygiene . .8vo, *i 75 

Palaz, A. Industrial Photometry 8vo, 5 00 

Palmer, A. R. Electrical Experiments i2mo, o 75 

Magnetic Measurements and Experiments i2mo, o 75 

Pamely, C. Colliery Manager's Handbook 8vo, *io 00 

Parker, P. A. M. The Control of Water 8vo, 600 

Parr, G. D. A. Electrical Engineering Measuring Instruments. .. .8vo, *3 50 
Parry, E. J. Chemistry of Essential Oils and Artificial Perfumes. 

Vol. I. Monographs on Essential Oils 9 00 

Vol. II. Constituents of Essential Oils, Analysis 7 00 

Foods and Drugs. Two Volumes. 

Vol. I. The Analysis of Food and Drugs 8vo, 

Vol.11. The Sale of Food and Drugs Acts. 8vo, 

and Coste, J. H. Chemistry of Pigments 8vo, 

Parry, L. Notes on Alloys 8vo, 

Metalliferous Wastes 8vo, 

— — Analysis of Ashes and Alloys 8vo, 

Parry, L. A. Risk and Dangers of Various Occupations 8vo, 

Parshall, H. F., and Hobart, H. M. Electric Railway Engineering . 4to, 

Parsons, J. L. Land Drainage 8vo, 

Parsons, S. T. Malleable Cast Iron 8vo, 

Partington, J. R. Higher Mathematics for Chemical Students. .i2mo, 

Textbook of Thermodynamics .8vo, 

The Alkali Industry 8vo, 

Patchell, W. H. Electric Power in Mines 8vo, 

Pat erson, G. W. L. Wiring Calculations i2mo, 

Electric Mine Signalling Installations i2mo, 

Patterson, D. The Color Printing of Carpet Yarns 8vo, 

Color Matcrnr.T 01 Textiles , 8vo, 

Textile Color Mixing 8vo, 



9 


50 


3 


50 


*5 


00 


*3 


50 


+2 


50 


*2 


50 


*3 


50 


7 


50 


*i 


50 


3 


50 


2 


50 


*4 


00 


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20 D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG 

Paulding, C. P. Condensation of Steam in Covered and Bare Pipes. 8vo, 

Transmission of Heat through Cold-storage Insulation, ...... nmo, 

Payne, D. W. Iron Founders' Manual 8vo, 

Peddie, R. A. Engineering and Metallurgical Books i2mo, 

Peirce, B. System of Analytic Mechanics 4to, 

Linear Associative Algebra 4to, 

Perkin, F. M., and Jaggers, E. M. Elementary Chemistry. .... i2mo, 

Perrin, J. Atoms . 8vo, 

Petit, G. White Lead and Zinc White Paints. t 8vo, 

Petit, R. How to Build an Aeroplane..... 8vo, 

Pettit, Lieut. J. S. Graphic Processes i6mo, 

Philbrick, P. H. Beams and Girders i6mo, 

Phin, J. Seven Follies of Science i2tno, 

Pickworth, C. N. Logarithms for Beginners i2mo, boards, 

The Slide Rule i2mo, 

Pilcher, R. B. The Profession of Chemistry i2mo, 

Pilcher, R. B., and Butler-Jones, F. What Industry Owes to Chemical 

Science i2mo, 

Plattner's Manual of Blow-pipe Analysis. Eighth Edition, revised . 8vo, 

Plympton, G. W. The Aneroid Barometer i6mo, 

How to Become an Engineer i6mo, 

Van Nostrand's Table Book i6mo, 

Pochet, M. L. Steam Injectors i6mo, 

Pocket Logarithms to Four Places i6mo, 

i6mo, leather, 

Polleyn, F. Dressings and Finishings for Textile Fabrics 8vo, 

Pollock, W. Hot Bulb Oil Engines and Suitable Vessels 8vo, 

Pope, F. G. Organic Chemistry 121110, 

Pope, F. L. Modern Practice of the Electric Telegraph 8vo, 

Popplewell, W. C. Prevention of Smoke ! 8vo, 

Strength of Materials 8vo, 

Porritt, B. D. The Chemistry of Rubber 121110, 

Porter, J. R. Helicopter Flying Machine i2mo, 

Potts, H. E. Chemistry of the Rubber Industry 8vo, 

Practical Compounding of Oils, Tallows and Grease 8vo, 

Pratt, A. E. Economic Metallurgy (In Press.) 

Pratt, Jas. A. Elementary Machine Shop Practice (In Press.) 

Pratt, K. Boiler Draught 12010, 

Prelini, C. Earth and Rock Excavation 8vo, 

Graphical Determination of Earth Slopes 8vo, 

Tunneling. New Edition 8vo, 

Dredging. A Practical Treatise 8vo, 

Prescott, A. B., and Johnson, 0. C. Qualitative Chemical Analysis. .8vo, 
Prescott, A. B., and Sullivan, E. C. First Book in Qualitative Chemistry. 

Prideaux, E. B. R. Problems in Physical Chemistry 8vo, 

The Theory and Use of Indicators 8vo, 

Prince, G. T. Flow of Water : . . . i2mo, 

Pull, E. Modern Steam Boilers 8vo, 

Pullen, W. W. F. Application of Graphic Methods to the Design of 

i2mo, 

Structures 121110, 

Injectors: Theory, Construction and Working 121110, 

Indicator Diagrams 8vo, 

Engine Testing „ 8vo, 



*I 


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D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG 21 

Purday, H. F. P. The Diesel Engine Design 8vo, 7 50 

Putsch, A. Gas and Coal-dust Firing 8vo, *2 50 

Rafter, G. W. Mechanics of Ventilation i6mo, o 75 

Potable Water i6mo, o 75 

Treatment of Septic Sewage i6mo, ) o 75 

and Baker, M. N. Sewage Disposal in the United States. .. .4to, 6 00 

Raikes, H. P. Sewage Disposal Works 8vo, *4 00 

Randau, P. Enamels and Enamelling 8vo, *5 00 

Rankine, W. J. M. A Manual of Applied Mechanics 8vo, 6 00 

Civil Engineering 8vo. 7 50 

Machinery and Millwork 8vo, 6 00 

The Steam-engine and Other Prime Movers 8vo, 6 00 

Rankine, W. J. M., and Bamber, E. F. A Mechanical Text-book. .8vo, 4 00 

Purday, H. F. P. The Diesel Engine Design 8vo (In Press.) 

Raphael, F. C. Localization of Faults in Electric Light and Power Mains. 

8vo, 5 00 

Rasch, E. Electric Arc Phenomena 8vo, 2 00 

Rathbone, R. L. B. Simple Jewellery 8vo, 2 50 

Rausenberger, F. The Theory of the Recoil Guns 8vo, *5 00 

Rautenstrauch, W. Notes on the Elements of Machine Design. 8vo, boards, *i 50 
Rautenstrauch, W., and Williams, J. T. Machine Drafting and Empirical 
Design. 

Part I. Machine Drafting. 8vo, 1 50 

Part II. Empirical Design (In Preparation.) 

Raymond, E. B. Alternating Current Engineering i2mo, 

Rayner, H. Silk Throwing and Waste Silk Spinning 8 vo, 

Recipes for the Color, Paint, Varnish, Oil, Soap and Drysaltery Trades, 

8vo, 

Recipes for Flint Glass Making i2mo, 

Redfern, J. B., and Savin, J. Bells, Telephones i6mo, 

Redgrove, H. S. Experimental Mensuration i2mo, 

Reed, S. Turbines Applied to Marine Propulsion ; *5 00 

Reed's Engineers' Handbook 8vo, 

— — Key to the Nineteenth Edition of Reed's Engineers' Handbook. .8vo, 

Useful Hints to Sea-going Engineers i2mo, 

Reid, E. E. Introduction to Research in Organic Chemistry. (In Press.) 
Reinhardt, C. W. Lettering for Draftsmen, Engineers, and Students. 

oblong 4to, boards, 1 25 
Reinhardt, C. W. The Technic of Mechanical Drafting, 

oblong, 4to, boards, *i 00 

Reiser, F. Hardening and Tempering of Steel nmo, 2 50 

Reiser, N. Faults in the Manufacture of Woolen Goods 8vo, 2 50 

Spinning and Weaving Calculations 8vo, *5 00 

Renwick, W. G. Marble and Marble Working. .. .8vo (Reprinting.) 

Reuleaux, F. The Constructor 4to, 4 00 

Rey, Jean. The Range of Electric Searchlight Projectors 8vo, 

(Reprinting.)- 

Reynolds, 0., and Idell, F. E. Triple Expansion Engines i6mo, o 75 

Rhead, G. F. Simple Structural Woodwork i2mo, *i 25 

Rhead, G. W. British Pottery Marks 8vo, 3 50 

Rhodes, H. J. Art of Lithography 8vo, 5 00 

Rice, J. M and Johnson, W. W. A New Method of Obtaining the Differ- 
ential of Functions i2mo, 50 



*2 


50 


*5 


00 


*5 


00 





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22 D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG 

Richards, W. A. Forging of Iron and Steel i2mo, 

Richards, W. A., and North, H. B. Manual of Cement Testing. . . . i2mo, 

Richardson, J. The Modern Steam Engine 8vo, 

Richardson, S. S. Magnetism and Electricity nmo, 

Rideal, E. K. Industrial Electrometallurgy 8vo, 

The Rare Earths and Metals 8vo (In Press.) 

Ozone 8vo, 

Rideal, S. Glue and Glue Testing 8vo, 

The Carbohydrates 8vo (In Press.) 

Riesenberg, F. The Men on Deck i2mo, 

Standard Seamanship for the Merchant Marine. i2mo (In Press.) 

Rimmer, E. J. Boiler Explosions, Collapses and Mishaps 8vo, 

Rings, F. Reinforced Concrete in Theory and Practice i2mo, 

Reinforced Concrete Bridges 4to, 

Ripper, W. Course of Instruction in Machine Drawing folio, 

Roberts, F. C. Figure of the Earth i6mo, 

Roberts, J., Jr. Laboratory Work in Electrical Engineering 8vo, 

Robertson, J. B. The Chemistry of Coal i2mo, 

Robertson, L. S. Water-tube Boilers 8vo, 

Robinson, J. B. Architectural Composition 8vo, 

Robinson, S. W. Practical Treatise on the Teeth of Wheels. .i6mo, 

Railroad Economics i6mo, 

Wrought Iron Bridge Members i6mo, 

Robson, J. H. Machine Drawing and Sketching 8vo, 

Roebling, J. A. Long and Short Span Railway Bridges folio, 

Rogers, A. A Laboratory Guide of Industrial Chemistry 8vo, 

• Elements of Industrial Chemistry i2mo, 

Manual of Industrial Chemistry 8vo, 

Rogers, F. Magnetism of Iron Vessels. i6mo, 

Rohland, P. Colloidal and Crystalloidal State of Matter 121110, 

(Reprinting.) 

Rollinson, C. Alphabets Oblong, i2mo, 

Rose, J. The Pattern-makers' Assistant 8vo, 

• Key to Engines and Engine-running nmo, 

Rose, T. K. The Precious Metals 8vo, 

Rosenhain, W. Glass Manufacture 8vo, 

Physical Metallurgy, An Introduction to 8vo, 

Roth, W. A. Physical Chemistry 8vo, 

Rowan, F. J. Practical Physics of the Modern Steam-boiler 8vo, 

and Idell, F. E. Boiler Incrustation and Corrosion i6mo, 

Roxburgh, W. General Foundry Practice 8vo, 

Rnhmer, E. Wireless Telephony 8vo, 

Russell, A. Theory of Electric Cables and Networks 8vo, 

Rutley, F. Elements of Mineralogy 121110, 

Rust, A. Practical Tables for Navigators and Aviators 8vo, 

Sandeman, E. A. Notes on the Manufacture of Earthenware. . i2mo, 

Sanford, P. G. Nitro-explosives 8vo, 

Saunders, C. H. Handbook of Practical Mechanics i6mo, 

leather, 

Sayers, H. M. Brakes for Tram Cars 8vo, 

Schaef er, C. T. Motor Truck Design 8vo, 

Scheele, C. W. Chemical Essays .8vo, 



2 


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4 


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*6 


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00 


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75 





75 


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00 


25 


00 


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D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG 23 

Scheithauer, W. Shale Oils and Tars 8vo, 

Scherer, R. Casein 8vo, 

Schidrowitz, P. Rubber, Its Production and Industrial Uses 8vo, 

Schindler, K. Iron and Steel Construction Works zamo, 

Schmall, C. N. First Course in Analytic Geometry, Plane and Solid. 

i2mo, half leather, 

and Shack, S. M. Elements of Plane Geometry i2mo, 

Schmeer, L. Flow of Water 8vo, 

Schwarz, E. H. L. Causal Geology 8vo, 

Schweizer, V. Distillations of Resins 8vo, 

Scott, A. H. Reinforced Concrete in Practice i2mo, 

Scott, W. W. Qualitative Analysis. A Laboratory Manual. New 

Edition 3 00 

Standard Methods of Chemical Analysis 8vo, 7 50 

Scribner, J. M. Engineers' and Mechanics' Companion. .i6mo, leather, 1 50 
Scudder, H. Electrical Conductivity and Ionization Constants of 

Organic Compounds 8v,o, 

Seamanship, Lectures on i2mo, 

Searle, A. B. Modern Brickmaking 8vo, 

• Cement, Concrete and Bricks 8vo, 

Searle, G. M. "Sumners' Method." Condensed and Improved. 

i6mo, 

Seaton, A. E. Manual of Marine Engineering 8vo, 

Seaton, A. E., and Rounthwaite, H. M. Pocket-book of Marine Engi- 
neering i6mo, leather, 

Seeligmann, T., Torrilhon, G. L., and Falconnet, H. India Rubber and 

Gutta Percha 8vo, 

Seidell, A. Solubilities of Inorganic and Organic Substances .... 8vo, 

Sellew, W. H. Steel Rails ( 4to, 

Railway Maintenance Engineering i2mo, 

S enter, G. Outlines of Physical Chemistry i2mo, 

Text -book of Inorganic Chemistry i2mo, 

Sever, G. F. Electric Engineering Experiments 8vo, boards, 

Sever, G. F., and Townsend, F. Laboratory and Factory Tests in Elec- 
trical Engineering 8vo, 

Sewall, C. H. Wireless Telegraphy 8vo, 

Lessons in Telegraphy . , . . , i2mo, 

Sexton, A. H, Fuel and Refractory Materials i2mo {Reprinting.) 

Chemistrv of the Materials of Engineering izmo, 

Alloys (Non-Ferrous) 8vo, 

Sexton, A. H., and Primrose, J. S. G. The Metallurgy of Iron and Steel. 

8vo, 

The Common Metals (Non-Ferrous) 8vo, 

Seymour, A. Modern Printing Inks , 8vo, 

Shaw, Henry S. H. Mechanical Integrators i6mo, 

Shaw, S. History of the Staffordshire Potteries .8vo, 

Chemistry of Compounds Used in Porcelain Manufacture. .. .8vo, 

Shaw, T. R. Driving of Machine Tools i2mo, 

Precision Grinding Machines icmo, 5 00 

Shaw, W. N. Forecasting Weather 8vo {Reprinting.) 

Sheldon, S., and Hausmann, E. Dynamo Electric Machinery, A.C. 

and D.C 8vo {In Press.) 

Electric Traction and Transmission Engineering. . . . ; nmo, 3 00 

Physical Laboratory Experiments, for Engineering Students. .8vo, 1 50 



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24 D. VAN NOSTRAND CO.'S SHORT TITLE CATALOG 

Sherriff, F. F. Oil Merchants' Manual and Oil Trade Ready Reckoner, 

8vo, 3 50 

Shields, J. E. Notes on Engineering Construction i2mo, 1 50 

Shreve, S. H. Strength of Bridges and Roofs 8vo, 3 50 

Shunk, W. F. The Field Engineer nmo, f abrikoid, 3 00 

Silverman, A., and Harvey, A. W. Laboratory Directions and Study 

Questions in Inorganic Chemistry 4to, loose leaf, 200 

Simmons, W. H. Fats, Waxes and Essential Oils. .8vo {In Press.) 
Simmons, W. H., and Appleton, H. A. Handbook of Soap Manufacture, 

3/o, 

Simmons, W. H., and Mitchell, C. A. Edible Fats and Oils 8vo, 

Simpson, G. The Naval Constructor i2mo, f abrikoid, 

Simpson, W. Foundations 8vo. {In Press.) 

Sinclair, A. Development of the Locomotive Engine. . . 8vo, half leather, 

Sindall, R. W. Manufacture of Paper 8vo, 

Sindall, R. W., and Bacon, W. N. The Testing of Wood Pulp. .. .8vo, 

Wood and Cellulose 8vo {In Press.) 

Sloane, T. O'C. Elementary Electrical Calculations i2mo, 

Small-wood, J. C. Mechanical Laboratory Methods. .. .i2mo, f abrikoid, 
Smith, C. A. M. Handbook of Testing, MATERIALS 8vo, 

Smith, C. A. M., and Warren, A. G. New Steam Tables 8vo, 

Smith, C. F. Practical Alternating Currents and Testing .8vo, 

Practical Testing of Dynamos and Motors 8vo, 

Smith, F. E. Handbook of General Instruction for Mechanics . . . i2mo, 

Smith, G. C. Trinitrotoluenes and Mono- and Dinitrotoluenes, Their 

Manufacture and Properties 121110, 

Smith, H. G. Minerals and the Microscope. 12-1110, 

Smith, J. C. Manufacture of Paint 8vo, 

Smith, R. H. Principles of Machine Work , i2mo, 

Advanced Machine Work i2mo, 

Smith, W. Chemistry of Hat Manufacturing i2mo, 

Snell, F. D. Colorimetric Analysis i2mo {In Press.) 

Snow, W. G., and Nolan, T. Ventilation of Buildings i6mo, 

Soddy, F. Radioactivity 8vo {Reprinting.) 

Solomon, M. Electric Lamps 8vo, 

Somerscales, A. N. Mechanics for Marine Engineers nmo, 

Mechanical and Marine Engineering Science 8vo, 

Sothern, J. W. The Marine Steam Turbine 8vo, * 

Verbal Notes and Sketches for Marine Engineers.. 8vo, 

Marine Engine Indicator Cards 8vo, 

Sothern, J. W., and Sothern, R. M. Simple Problems in Marine 

Engineering Design i2mo, 

Souster, E. G. W. Design of Factory and Industrial Buildings. . .8vo, 

Southcombe, J. E. Chemistry of the Oil Industries 8vo, 

Soxhlet, D. H. Dyeing and Staining Marble ' 8vo, 

Spangenburg, L. Fatigue of Metals i6mo, 

Specht, G. J., Hardy, A. S., McMaster, J. B., and Walling. Topographical 

Surveying i6mo, 

Spencer, A. S. Design of Steel-Framed Sheds 8vo, 

Spiegel, L. Chemical Constitution and Physiological Action nmo. r 25 



*4 


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D. VAN NOSTRAND GO.'S SHORT-TITLE CATALOG 25. 

Sprague, E. H. Hydraulics . .............. .i2mo, 200. 

Elements of Graphic Statics 8vo, 3 co 

Stability of Masonry iamo, 2 00 

Elementary Mathematics for Engineers i2mo, 2 00 

Stability of Arches i?.nio, 2 00 

Strength of Structural Elements i2mo, 2 00 

Moving Loads by Influence Lines and Other Methods i2mo, 2 00 

Stahl, A. W. Transmission of Power i6mo, 

Stahl, A. W., and Woods, A. T. Elementary Mechanism i2mo, 2 25 

Standage, H. C Leatherworkers' Manual. . . . 8vo, 4 50 

Sealing Waxes, Wafers, and Other Adhesives 8vo, *2 50 

Agglutinants of All Kinds for All Purposes i2mo, 3 50 

Stanley, H. Practical Applied Physics {In Press.) 

Stansbie, J. H. Iron and Steel 8vo, 2 50 

Steadman, F. M. Unit Photography 121110, 2 50 

Stecher, G. E. Cork. Its Origin and Industrial Uses i2mo, 1 00 

Steinheil, A., and Voit, E. Applied Optics., Vols. I. and II. 8vo, 

Each, 5 00 

Two Volumes Set, 9 00 

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*3 50 


1 


50 


2 


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10 


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15 


00 





75 


1 


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*3 


00 


*2 


25 


*3 


00 


*3 


50 


*3 


50 


*i 


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*3 


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*2 


50 


*4 


00 





75 


2 


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*3 


00 


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2 


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*2 


00 


12 


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*0 


75 


*I 


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6 


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2 


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75 





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